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 ...
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1 answer
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How to get the explicit example of existence from Reduce?

I have the following Reduce: ...
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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&...
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2 answers
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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. ...
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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 votes
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Helping Reduce solve an exist statement

I have the following Reduce problem: ...
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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. ...
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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 ...
1 vote
1 answer
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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 ...
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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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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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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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1 answer
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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 views

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\...
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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: ...
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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 votes
1 answer
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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 ...
2 votes
1 answer
106 views

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: ...
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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?
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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 $\...
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How to formula the left side of the equation and move the constant term to the right side of the equal sign. Form such equation form?

...
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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 ...
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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 ...
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1 answer
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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 answers
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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? ...
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1 answer
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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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2 answers
90 views

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 ...
2 votes
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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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 <...
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2 votes
2 answers
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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: ...
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1 answer
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FindRoot and indeterminate expression

I have tried the following with several different starting points and always returns errors: ...
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0 answers
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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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Solving for unknowns that are related

For this code: ...
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1 answer
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Solving equation with FindRoot

I have: ...
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0 votes
1 answer
48 views

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 ...
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2 answers
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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 ...
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3 votes
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 answers
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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 $p_i \approx \exp(p_i-1)$...
2 votes
1 answer
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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 votes
2 answers
327 views

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,\...
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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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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
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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....
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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 ...
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4 votes
3 answers
148 views

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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4 votes
3 answers
136 views

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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