Questions tagged [equation-solving]
Questions on the analytic and numerical equation solving functions of Mathematica (Solve, Reduce, NSolve, FindRoot, DSolve, RSolve, etc.).
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Solving a system with Exponential equations [closed]
Given the following system
\begin{align*}
2\cdot 3^x-3 \cdot 2^y&=-22\\
5\cdot 3^x+\frac{1}{2}\cdot2^y&=9
\end{align*}
TThen let $w=3^x$ and $u=2^y$
\begin{aligned}
2\cdot w-3 \cdot ...
2
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1
answer
44
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3
votes
1
answer
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Difficulty to Solve the Generalized Wave Equation
Given the following problem
$$u_{tt}-\frac{v}{2}\cdot u_{xx}+\frac{v}{2}\cdot x^2 \cdot u(x)=0 $$
$$u(x,0)=f(x)$$
$$u_t(x,0)=g(x)=0$$
Where $ f(x)=y_0(x) $
$y_n$ are the Eigenfunctions that defined ...
2
votes
1
answer
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Invalid PeriodicBoundaryCondition for Navier Stokes problem using NDSolveValue
Background: I'm looking to have a 2D re-entrant channel of a geophysical flow that is forced by a wind stress at the surface ("taux"; below) and experiences planetary rotation ("cor&...
- 21
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2
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Don't understand an evaluation with BezierFunction
I don't understand the source of the failure of the following attempts to solve an equation involving the following very simple BezierFunction.
...
- 13k
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How apply FindRoot with a function that is Infinity on one side? CoolProp challenge
Background: The humid air CoolProp wrapper HAPropsSI for Mathematica does not seem to accept both the humidity ratio "W" and relative humidity ratio "...
2
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answers
54
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1
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Solving equations involving elliptic functions [duplicate]
I have this:
sol = a^2 + b^2 - c^2 + 2 (c^2 - a^2)*JacobiDN[Sqrt[c^2 - a^2]*x, m] ==
u /. {m -> 1}
And I want to find its inverse, i.e. express x in terms of u. ...
- 157
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1
answer
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Finding the inverse function when we have Jacobi functions? [closed]
I have this function
u = JacobiDN[Sqrt[b^2 - q^2]/k*k*x, m] /. {m -> 1}
And I want to find the inverse, i.e., give it in terms of x instead of u
I'm finding the ...
- 157
1
vote
1
answer
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+100
How to solve the problem with the error in FindRoot for non-linear equation?
Whoever is reading this have to be patient as the code is slightly long and I have explain each section in order to explain the problem. So I want to solve the set of non-linear algebraic equation ...
- 471
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85
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Plot Generalized Heat Equation
Given the following problem
$$u_{t}-\frac{v}{2}\cdot u_{xx}+\frac{v}{2}\cdot x^2 \cdot u(x)=0 $$
$$u(x,0)=f(x)$$
Where $ f(x)=y_1(x)+0.2y_4(x)+0.01y_6 (x) $
$y_n$ are the Eigenfunctions that defined ...
2
votes
2
answers
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Finding the point where the two roots are equal from Finding Root
k[r_, a_, \[Alpha]_] = a^2 + r (r - 2) + r^2\[Alpha] Exp[-2r/\[Alpha]];
FindRoot[ k[r, 0.9,0.4]==0,{r,2}];
...
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answers
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Sturm-Liouville Problem
Given the following BVP
$$-(e^x Y'(x))'=\lambda e^x Y(x), \quad 0<x<\pi$$
$$Y(0)=0, Y(\pi)=0$$
I have found that the eigenfunctions are
$Y_n(x)=e^{-\frac{x^2}{2}}\sin{nx}$
and the eigenvalues ...
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1
answer
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Dsolve to find vector potential component's
I want to find the vector potential component's. I expand the Poisson’s equation in cylindrical coordinates which yields the three equations as in the picture. The equation along rho direction equal ...
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2
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1
answer
162
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Analytical Solution in Generalized Heat Equation
Given the following problem
$$u_{t}-\frac{v}{2}\cdot u_{xx}+\frac{v}{2}\cdot x^2 \cdot u(x)=0 $$
$$u(x,0)=f(x)$$
Where $ f(x)=y_1(x)+0.2y_4(x)+0.01y_6 (x) $
$y_n$ are the Eigenfunctions that defined ...
3
votes
3
answers
228
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Intersection points of two-variable polynomials
Let $h$ and $g$ designate two multivariable polynomials:
$$\!\!h(x,y)=-96\! \left(32 x^2\!+\!8 x (3\!-\!8 y)\!+\!40 y^2-28 y+5\right) \left(10 x^2+x (4 y-2)+\quad\quad\quad\\ \quad\quad+(1-2 y)^2\...
- 159
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1
answer
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On the solution of systems equations with exact coefficients
It all starts with the following system of equations that I can't solve by hand:
...
- 4,402
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0
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50
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How to find output response of filter circuit if transfer function is too complex?
I want to find unit step response of this transfer function. But I think, there is a problem, mathematica is not given any solution. Can anybody give me suggestion how to get the output response?
<...
3
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1
answer
82
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Steady state fluid flow for downward flow past an obstacle
I was attempting to simulate fluid flow past a circular obstacle. The following is the code which I used
...
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2
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1
answer
106
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Another solution to a simple DE given by DSolve: not the one I expected
Consider a simple 2nd-order differential equation with a parameter $a$, which can be solved with DSolve:
...
- 1,217
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1
answer
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Solving series solution of differential equation
AsymptoticDSolveValue[2x*y''[x] -(3+2x)*y[x] +1 == 0, y[x], {x, 0, 5}], this differential equation command, is not outputting the correct solution. The solution should be like y=C1(1+(1/3)x-(1/6)x^2-(...
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Finding only non-negative roots with FindRoot
Given an arbitrary function F, how do I force FindRoot to look only for non-negative roots, returning nothing otherwise?
- 4,362
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How to use quasi-Newton methods to solve a non-linear system?
Consider the following function, for $\mathbf{x}=\{x_1,...,x_n\}$
$$
F(\mathbf{x})=\sum_{k=0}^n \frac{e^{A_k\mathbf{x}}-e^{B_k\mathbf{x}}}{C_k\mathbf{x}}-\mathbf{b}
$$
where $\{A_k\}$, $\{B_k\}$ and $\...
- 4,362
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1
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How to divide the same number on both sides of the equation?
The given equation is:
y^2 (1 - λ^2) +
a^2 λ^2 (-1 - (λ^2 (1 - λ^2))/(-1 + \
λ^2)^2) + (1 - λ^2) (x - (
a λ^2)/(-1 + λ^2))^2 == 0
Note that this type of ...
- 797
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1
answer
33
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Modified Rational approximant of a polynomial (v2)
ok this time I will try to post only the essential information, I hope it doesn't end like the previous thread.
the objective is similar to the previous one but now I cannot use the Padèapproximant ...
- 2,549
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votes
1
answer
42
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How to extract the ratio between two variables in a linear system?
I am trying to solve a simple linear system using Mathematica (see the image below). I understand there are five variables (A1, A2, B1, B2, A3) and only four equations, so I cannot solve them. I want ...
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2
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Why is it possible to solve this equation by setting a greater than 0 and not equal to 0?
Why is there no solution for the system of equations with a greater than 0?
...
- 797
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Solving polynomial equation of 4th order with more than 1 variable
I have this equation but it takes so long and no answer comes out. Could you please suggest me what to do or should I just wait more. Even if you could help me understand different numerical solves, ...
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votes
2
answers
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How to square the left and right sides of an equation at the same time？
There is an equation :
-2 == Sqrt[x^2 + (-2 - y)^2] - Sqrt[x^2 + (2 - y)^2]
There are two radicals on the right side of equal to coincidence，The following are ...
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How to find a conditional solution of inequalities?
Im trying to find the conditions of:
a>0,b>0,c>1,d>0
(a + (2 a - b/c) d + (a + b - b/c) d^2 + (-b + (2 b)/c) d^3 + (b d^4)/
c - (b d^5)/c) > 0
I ...
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2
answers
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Solve can’t solve this… is there a way to approximate it?
I've been toying around with mortgage/loan calculations and spreadsheeting. The loan formula is as follows:
A = p * r *(1+r)^n / ((1+r)^n - 1)
A: payment per period
p: principal
r: interest rate
n: ...
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1
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Is there any hope to compute analytically $y=f(x)$ for which $g(x,y)=0$?
I have a two-variable function $g(x,y)$ with $0<x\leq\frac{\pi}2$ and $\frac32<y<5$. I am looking for $y=f(x)$ for which $g(x,y)=0$. Using ContourPlot
<...
- 1,159
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Plotting solutions of a difference equation
I'm trying to reproduce Figure 2 of this paper.
This plot is the solution of Eq. (7) of the paper, which is a difference equation, with an initial value given in Table 1. Here is its summary:
...
user91712
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votes
1
answer
68
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FindRoot and indeterminate expression
I have tried the following with several different starting points and always returns errors:
...
user91712
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0
answers
34
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How to make CholeskySolve function faster to execute?
I would like to ask about the solution of [A]{x}={B}. As you know {x} can be obtained by Inverse[A].{B} However, when the dimension of [A] is so large, i.e, dimA=100000, then the inverse function ...
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1
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Can Print no longer access certain values during evaluation? [duplicate]
This example from Power Programming in Mathematica doesn't work for me anymore: the values used for rootfinding are not printed during evaluation. What changed? Is there a new way to reproduce the old ...
- 1,706
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votes
2
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42
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Problem with "Solve" in Mathematica [closed]
I have the following Equations
a11 = D[R T Exp[-a/(R T V)]/(V - b), T];
a21 = D[R T Exp[-a/(R T V)]/(V - b), {T, 2}];
When I use ...
- 333
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1
answer
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Solve not working with cross product with units
I recently asked this question about using Solve with cross product.
Solve not working when doing cross-product
When I use the units in the definition of the variables, I am not able to get an answer.
...
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2
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Solving $\sum_i a_i p_i^k=b_0$ for $k$
Is there a fast way to find $k$ in the equation below for positive reals $a_i,p_i,b_0$?
$$\sum_i^d a_i p_i^k=b_0$$
Constraint of the problem means $p_i$ is very close to 1, so $p_i \approx \exp(p_i-1)$...
- 6,847
2
votes
1
answer
50
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Using the result of Solve as a function of parameters
I am trying to find b2 maximising a function I named 'EG1EUB'. And 'EG1EUBb2' is the frist order condition. Based on my understanding, Solve gave me a single solution saying that b2 is the second root....
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3
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2
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How to solve transcendental coupled equations?
Dear Mathematica users,
I am trying to solve the following system of transcendental equations,
$$
f(\eta,y,\theta) = y - \frac{2}{\eta}{\textrm{Coth}(\frac{3 y \eta}{4 \theta})}=0,
$$
$$
g(\eta,y,\...
- 447
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votes
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answers
39
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Solve function is taking a long time to run
I'm trying to solve two equations using Solve. For one of them (input 68) it worked perfectly. However, for another equation that is solved with the same structure (...
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1
answer
62
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How can I plot a function of NSolve results?
A seemingly simple question. I have an equation with a free parameter. There is no explicit solution, so I plot the numerical solutions as functions of the parameter.
...
4
votes
2
answers
233
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Solving two equations simultaneously and ploting the result
I have:
$$p_n = \frac{e^{-a/n - bn}}{\sum_{n = 3}^{12} e^{-a/n - bn}},$$
where $a$ and $b$ are unknown. I have also given: $\langle n \rangle = \sum_{n=3}^{12} n p_n = 6$.
Now, I need to plot $p_n$ vs....
user90644
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Nonlinear equations with Differential Evolution and Newton-Raphson
Don't kill me, please, but I'm here again with a new toy code. In particular, it's a routine which, given a system of non-linear equations as input, randomly searches for very crude candidate real ...
- 4,402
4
votes
3
answers
148
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Simplifying an expression to a sensible conic section polynomial
I have an expression which represents an intersection of the unit sphere and a cone, projected to two-dimensional plane:
...
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How to numerically solve a differential equation which has integration in it?
I am trying to solve the following differential equation which has integration in it. It is not giving any results. Can anyone help?
...
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