Questions tagged [equation-solving]
Questions on the analytic and numerical equation solving functions of Mathematica (Solve, Reduce, NSolve, FindRoot, DSolve, RSolve, etc.).
6,494
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FindRoot with input as a list
I have three equations: eq1, eq2, eq3 with variables a,b,d,k. I wish to find the roots of these equations by assuming ...
-1
votes
1
answer
91
views
Adding Points on an Elliptic Curve
How do I do this in Mathematica?
The curve given by the equation $y^2 = x^3 + 29x + 7$ defined over the integers modulo $10007$
Adding the first pair of points $P = (3737, 4549)$ and $Q = (8286, 6097)$...
2
votes
3
answers
242
views
Getting all solutions to an equation on condition the variables are either 0 or 1
Given a list of 3-bit binary lists
b={{0,0,0},{0,0,1},{0,1,0},{0,1,1},{1,0,0},{1,0,1},{1,1,0},{1,1,1}};
I would like to have all possible solutions to
...
1
vote
1
answer
246
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Numerical solving diffusion equation in spherical coordinates
Mathematica nicely solves Poisson's equation in spherical coordinates as
...
1
vote
1
answer
54
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First order differential equation with two conditions
I want to produce all possible solutions for this equation:
...
1
vote
1
answer
63
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Problems with Solve. Only works for specific parameters. Solve function do not "start"
I have the following problem I want to solve the following equalities.
My used code:
...
2
votes
1
answer
150
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How to solve this integral equation numerically?
I am encountering difficulties while trying to numerically solve an equation in Mathematica that involves an unknown function and an integral. Specifically, the equation takes the form of
\begin{...
2
votes
2
answers
84
views
Selecting Solve results according to conditions
When using the Solve function I get four possible answers. How can I automatically get the option in which x and y are positive? Where to insert the conditions x>=0 and y>=0?
...
1
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2
answers
159
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How can I choose the integer numbers a, b, c, d, t so that the equation $\sqrt{a x^2+b x+c}=d x+t$ has two integer solutions?
The equation $\sqrt{x^2+36 x+180}=2 x+15$ have two integer solutions are $x = -5$ and $x = -3$. How can I choose the integer numbers $a, b, c, d, t$ so that the equation $\sqrt{a x^2 + b x + c} = d x +...
1
vote
0
answers
63
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Why this Solve cannot be solved [duplicate]
Solve[Sum[p*a[i], {i, 1, n}] == 0, p, Reals]
Solve[p*Sum[a[i], {i, 1, n}] == 0, p, Reals]
The first line of code cannot be solved, but when the variable ...
3
votes
2
answers
105
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Solving A System of Two Implicit Equations
I am solving a system of 6 equations, and I am interested to know the solution for different rhoBar values. Here is the input parameters:
...
0
votes
2
answers
54
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Can a redundant condition be removed from a solution?
A solution to this equation:
Solve[{(p-x)^2 + (q-y)^2==d, p/q==t}, {p,q}, Reals]
has this repetitive condition:
$\displaystyle\quad d > \frac{x^2 - 2txy+t^2y^2}{...
0
votes
1
answer
51
views
How can i create an equation with a sum? [closed]
I have a list of $p_i$ and the condition that $\sum_{i=0}^{i=69} p_i = 1 $
I also have a list of 69 other different equations. I want to use NSolve to solve for the ...
1
vote
1
answer
105
views
How to find the variable $k$ which minimizes the function $\Omega^2$?
$$\Omega^2(k) = 4(\sum\limits_{m=1}^{\infty}\frac{1-\cos(km)}{m^{1+\alpha}})(\sum\limits_{m=1}^{\infty}\frac{1-\cos(km)}{m^{1+\alpha}} - A^2)$$
Let $A = 1$ and $\alpha = 1$ and write $w(k) := \sum\...
0
votes
0
answers
55
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Get curve equation from parametrization
I am quite new to Mathematica and I have been wondering how to do this one very specific thing.
I have two functions $x(t)$ and $y(t)$ that are the parametrization of a curve, how would I get the ...
0
votes
2
answers
86
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`Reduce` is running forever
I'm trying to solve the last inequality in Reduce in the code below in terms of rmax under the parameter conditions included in <...
0
votes
0
answers
59
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How to speed up maximization of the Solve output?
I am trying to maximize the solution of the system of algebraic equations for different values of parameters. The problem is related to the absorbing times in Markov chains.
Here is the code
...
3
votes
1
answer
150
views
Cannot solve this polynomial equation
I'm trying to solve the following polynomial equation for $x$:
$$ (qx)^\alpha (1-qx)^{1-\alpha} = [(1-q)x]^\beta [1-(1-q)x]^{1-\beta} $$
where $\alpha, \beta, q, x$ are all strictly between 0 and 1.
...
2
votes
3
answers
143
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Multiple solutions from NSolve
I have a list of polynomial equations which I can solve using NSolve. However, it gives me a large number of similar solutions. The solutions are largely identical ...
1
vote
1
answer
70
views
Solving a non-algebraic equation at the symbolic level [closed]
Versions 10, 11, 12, 13.0.0.0 and 13.2.0.0 solves the following system of equations
...
1
vote
1
answer
68
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Newton Raphson apply to Van der Waal Equation
I need assistance with this problem. I have two functions, where f1 corresponds to the dimensionless van der Waals equation of state, and function 2 corresponds to the dimensionless chemical potential ...
1
vote
1
answer
65
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Find an instance satisfying equation
I have the following equation with two variables xi and nu.
...
0
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1
answer
30
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Solving Nonlinear Algebraic Equation
What is wrong with the code below? Mathematica is taking a long time trying to solve it.
...
0
votes
1
answer
74
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Solving inequality with `Reduce` doesn't work
I'm trying to solve an inequality in terms of one variable under some conditions for parameter. Here is the code.
...
0
votes
1
answer
122
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Newton-Raphson Method Errors
I need assistance with this problem. I have two functions, where f1 corresponds to the dimensionless van der Waals equation of state, and function 2 corresponds to the dimensionless chemical potential ...
2
votes
2
answers
189
views
Real zeros of complex function
I must find the zeros of a complex function $\xi$ that depends upon two real variables $B$ and $k$. The function is obtained by evaluating the determinant of the identity matrix of dimension $2n$ ...
1
vote
0
answers
71
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How to solve differential equations in just in reals? [closed]
I am working on a variation problem:
My goal is to find the curve that connects a point $(x_1, y_1)$ to another point $(x_2, y_2)$. When this curve is revolved around the x-axis, it should generate a ...
0
votes
2
answers
122
views
Limit the number of the results returned by Solve to some specific number
I have this Solve:
...
1
vote
2
answers
131
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How to solve this integro-differential equation in Mathematica?
I am a new user of Mathematica, and I am trying to figure out how to solve the following integro-differential equation in Mathematica:
$\frac{\partial c(x,t)}{\partial t} = -2 \mu x c(x,t) + 4 \mu \...
0
votes
1
answer
130
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Solve[] isn't producing a correct result
I want to find the exact algebraic roots of the following function in terms of Z, P, Q, <...
0
votes
1
answer
61
views
Is it possible to get rid of the square root in the solutions of the following symbolic quadratic equation?
I have a quadratic equation, which I want to solve, but don't want the square root to appear within the solutions. I tried converting the discriminant into a quadratic form but failed, not sure if ...
0
votes
0
answers
59
views
How does Mathematica select principal roots of complex numbers?
When I do
I^(1/3)
I get
Out[]:= (-1)^(1/6)
which is one of the solutions of $z^3=i$. There are two more solutions which are ...
3
votes
1
answer
154
views
Solving system of first order PDEs
I am trying to solve the 1st order PDE system
\begin{align}
\xi_u^2+\eta_u^2&= \left(1+\frac{\xi^2+\eta^2}{4} \right)^2\\
\xi_v^2+\eta_v^2&=\left(1+\frac{\xi^2+\eta^2}{4} \right)^2
\end{align}
...
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votes
1
answer
50
views
How to convert the equation into this two forms?
The equation is:
x0^2/a^2 - y0^2/b^2 == 1
How to convert to this two forms:
b^2 x0^2 - a^2 y0^2 -> a^2 b^2
and
...
1
vote
0
answers
86
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Attempt to find a solution (out of potentially many) to a system of equations with FindInstance runs forever or crashes
I have a system of equations that in principle should have a solution (I would think not a unique one), which I want to solve. I am not interested in all solutions; I just want to locate one, assuming ...
1
vote
0
answers
63
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Computing Displacement Potential functions
I am new to Mathematica.
I am trying to compute the displacement Potential functions. My code is as follows.
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0
votes
2
answers
57
views
How to interpret the solution and how to work with it further?
Please help me understand the solution to the following problem:
...
1
vote
1
answer
82
views
Minimization of an implicitly specified function
exp - an experimental data, where expT - temperature, expChi - magnetic susceptibility
I ...
1
vote
1
answer
215
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How to simplify? [closed]
The original formula is:
Abs[(a b)/x0]/(2 Sqrt[1 + y0^2/x0^2])
How do you convert operations to get this result?
...
0
votes
1
answer
89
views
How can the process of hyperbola problems achieve the desired results?
As shown in the picture above, in the hyperbola x^2/a^2-y^2/b^2==1, point P is any point on the hyperbola, through the point P respectively do two asymptotes of the hyperbola parallel line PA, PB. The ...
0
votes
3
answers
106
views
Calculate Bernoulli numbers ( with a twist) [closed]
Mathematica has an inbuilt function BernoulliB that calculates $B_n$ for which,
$$\frac{t} {\left(e^t-1\right)}=\sum_{n=0}^{\infty} \frac{B_n}{n !}t^n $$
I need to ...
0
votes
1
answer
50
views
How do I plot a 2D function with an intermediate variable?
I have a function
$c\cdot\frac{x^2}{x^2 + 10^{-6.367}*x + 10^{-6.367-10.32}} + x = c\cdot\frac{10^{-6.367-10.32}}{x^2 + 10^{-6.367}*x + 10^{-6.367-10.32}}+\frac{10^{-14}}{x}$, where $0 < x < 10^{...
0
votes
1
answer
127
views
Kernel Crash Using Solve
The following code crashes the Kernel with no error message.
...
2
votes
1
answer
51
views
A matrix given by some parameters and variables. How to determine those parameters so that the matrix is independent of all variables?
For example, I have a matrix A given by some parameters (a,b,c,d) and two variables (x,y),
$$
A=\begin{pmatrix}a&a+bx\\(c-d)y&a(c+d)\end{pmatrix}
$$
The condition is that A is a matrix ...
0
votes
0
answers
94
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Solve does not find solutions to large equation rotation matrix
I've been seeing some posts already where people mention Solve needs a bit of help to get things solved in some scenarios.
I have been trying to figure out the solutions for equations. For the XYZ ...
1
vote
1
answer
63
views
How to get the range of t value in a Manipulate for trajectories?
How would I find the final time for different v and theta values so that the range of t in the manipulation would change for different v and theta values?
...
0
votes
1
answer
97
views
How to extract fixed factors after equation term shift?
The equation given is:
y - y1 == (y1 - y2)/(1 - x2) (x - 1)
How to transfer y1 to the right side of the equation and extract the common factor (y1 y2)/(1 x2) to ...
0
votes
0
answers
99
views
How to solve recurrence equation using RSolve?
How can I solve the following recurrence equation while I dont have the initial values?
Is it possible to solve this using RSolve?
...
2
votes
1
answer
105
views
How to code retarded time in Lienard-Wiechert potential equations?
I have been making strides on my project with the help of others here but have run into another snag: I am having difficulty in expressing the Lienard-Wiechert potentials with retarded time. For ...
2
votes
2
answers
105
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NDSolve of a non-linear ODE
I am trying to solve the following non-linear ODE numerically:
...