Questions tagged [equation-solving]
Questions on the analytic and numerical equation solving functions of Mathematica (Solve, Reduce, NSolve, FindRoot, DSolve, RSolve, etc.).
5,060
questions
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Solving a complex equation analytically
In my attempt to find a solution to my own question over at CrossValidated, I want to solve the following equation for $p$:
$t^2=p^2\left[1 - \frac{m}{p}Y-Y^2\right]$
where
$Y=\frac{\frac{1}{\sqrt{2\...
3
votes
1answer
83 views
Find centre of spiral similarity of two lines
I am trying to find a formula for the centre of spiral similarity (see here) of two lines, lineAB and lineCD. My problem comes ...
0
votes
0answers
42 views
How can I know what is # in equation? [duplicate]
I am trying to find the solution by using Reduce to fit my data with FindFit. And I don't know what ...
0
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1answer
34 views
Solve multiple equations with a parameter by means of Reduce
I have developed a program that solves an equation and give its solutions as outputs:
...
1
vote
1answer
62 views
Avoiding/skipping singularity error in ParametricNDSolve
I've looked up a few examples of similar errors for ODE's with singular points, but have yet to figure out a way to solve this problem for my case. A simple patch up where the singular point is '...
0
votes
1answer
81 views
Plot the phase portrait of a differential equation by using StreamPlot
How can I plot phase portrait by using different initial conditions? Are these conditions already specified when I choose the min and max values in the StreamPlot command? I will post the equation ...
5
votes
3answers
202 views
How to Solve Functional Differential Equation
I tried to solve this equation numerically.
eqnEx = x''[t] + x[2 t] == 0;
NDSolve[{eqnEx, x[1] == 10, x'[1] == 0}, x[t], {t, 1, 10}]
Two important character of the ...
0
votes
0answers
39 views
Compile and NSolve
Consider the following numerical problem. One deals with transcendental complicated function f that depends on several parameters and three variables, say ...
0
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0answers
32 views
Solving for a few roots in the neighborhood of an initial point for an eigen-equation with many roots
I have a system that is described by a complex matrix, $U$, which is a function of two parameters $f, \beta$ (a dispersion eigen-relation in wave physics). We are interested in the solutions ($f,\beta$...
1
vote
1answer
63 views
How to solve integro-differential with parameters iteratively?
I am trying to solve an integro-differential equation and tried using one of the answers that I found in a related question:
Numerically solve an integro-differential equation
The difference is I have ...
3
votes
3answers
203 views
Finding the enclosed area between two equations
I have to find the sum of the enclosed area between two functions that goes from 0 to 2pi:
...
0
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0answers
48 views
Strange behavior of FindInstance
I try to solve a problem from Kazakhstan math school competition (see it here in Russian) by
...
1
vote
1answer
66 views
How does Mathematica solve this system of nonlinear equations?
During a calculation for a physics lab, I ran into the following six non-linear equations with unknowns $x_1,x_2,x_3,x_4,x_5,x_6 \in \mathbb{R}$
...
0
votes
1answer
69 views
How to get Sum of array of integers?
This question seems easy but I am struggling with it now, I tried a few ways and check this solution as well but couldn't help me, please check and help if you are able:
So I need to save the sum of ...
0
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0answers
47 views
How to simplify sqrt without imaginary unit
I've a system of equations and one solution that Mathematica throws is:
$$ x=\frac{\mathbb{I} b \sqrt{pA - pS}}{\sqrt{-3 pA + 3 pS}}$$
knowing that $pS,pA \in \mathbb{R}$ and allways
$$ pS > pA $$
...
0
votes
1answer
26 views
Using Simplify and Reduce with Assumptions when the inequality is already one of the assumptions
I am using the Simplify and Reduce functions to reduce inequalities, but somehow the function Simplify does not consistently give "True" when the inequality happens to be one of the ...
1
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0answers
114 views
How to solve a system with infinitely many equations?
I need to solve the following system of (infinitely many) equations. I am looking for $V(0,0)$
$t \in \{0,1,2.....\}$ with one caveat that $s \leq 1+t$ should hold.
$ s \in \{1,2,3,L-1\}$
fixed ...
0
votes
3answers
87 views
Findroot and plot not showing line
I need help solving this equation
$$2- 12 sin(3 x) - 6 x = 0$$
using FindRoot, but it does not seem to work.
For example,
...
1
vote
0answers
59 views
how can I get an expression in the form of another expression
I need help solving this equation, I have done it by hand, but it is not very efficient to do.
Express |z-i|=2|z+1| in the form |z+a|=b, where z ∈ C and a ∈ C and b ∈ R+
I used this:
...
1
vote
1answer
74 views
Modelling transparent boundary conditions on a three-bonded quantum graph
I've created two issue last year, but unfortunately was able to return to this problem only now.
This question is a continue to this issue.
Essentially I am now trying to apply a solution from the ...
4
votes
1answer
345 views
Some doubts about symbolic equations in Wolfram Mathematica
I need to perform the following operations using Wolfram Mathematica.
I have these equations:
$$a b = c+d+e$$
$$\frac{d}{f}=g h + i$$
$$k=\frac{a}{c}$$
I need to obtain $k$ as a function of: $a,b,c,e,...
0
votes
1answer
43 views
Partial derivative on a Solve solution
Trying to solve a demand-supply equilibrium here and them find a partial derivative of the equilibrium with respect to the parameters.
...
2
votes
1answer
95 views
Getting Mathematica to solve a system of two second order nonlinear ordinary differential equations
I tried solving a system of two second order nonlinear ordinary differential equations using the DSolve command.
First, I tried like this:
...
0
votes
1answer
52 views
4
votes
1answer
54 views
Why does Reduce give False on SameQ with its copy-pasted result?
If I evaluate
Reduce[#, x] & /@ {{4 x > 1, 2 x < 5}, {5 x > 1, x < 5}, {4 x > 1, x < 5}}
the result is
...
2
votes
1answer
55 views
Does FindInstance traverse the entire domain?
If the result of FindInstance[expr<=0,vars,dom] is empty set, can it mean that expr is always greater than ...
4
votes
1answer
108 views
Square root problem
Consider the following code
NDSolveValue[{
x'[t] == x[t]^a,
x[0] == 0
}, x, {t, 0, 10}]
which solves the equation $x'(t)=x(t)^a$, for some exponent $a$, with ...
1
vote
1answer
75 views
Optimization of second order ODE with more than one parameter
I want to optimize a second order ODE with more than one variable:
...
-1
votes
0answers
43 views
Solve a system of algebraic equations
I'd like to determine whether there exist $\beta>0$, $A_i(i=1,\cdots,5)$, $B_i(i=1,\cdots,4)$, $C_i(i=1,\cdots,3)$, $D_i(i=1,2)$, and $G_1\in\mathbb{R}$,such that these parameters satisfy the ...
0
votes
1answer
30 views
testing linear independence for an unknown number of matrices
I would like to test if 16 matrices (4X4) that I created are linearly independent. The straight-forward solution would be to check if the equation
$\sum_{k=1}^N \alpha_k A_k = 0$ (1) (N=16 in the ...
0
votes
1answer
59 views
Solving an equation, and verifying that it is correct
I want to solve the equation
Solve[e == 1/2 (-2 ef + hvk - Sqrt[9 hvk^2 + 4 j^2]), hvk]
I then obtain the solutions
...
0
votes
1answer
55 views
Is it possible to ask Mathematica to give all the roots of the given function?
I have this equation
$$ 36 \cos \frac{3 x}{4} \cos \frac{27 x}{20} \left(\cos \frac{3 x}{5} +2 \cos \frac{21 x}{10} \right)=0 $$
Is it possible to ask Mathematica to give all the roots of the ...
0
votes
0answers
68 views
Can Mathematica solve this exponential equation
My version (12.1.0.0 Student Edition) does not solve this equation:
Solve[Exp [-n^2/(2 m)] <= 3/4, m]
WolframAlpha finds the solutions, but only for integer n? ...
0
votes
0answers
45 views
Hi. I'm a beginner so I need help to solve this equations using Regula-Falsi to find root of the equation (which is x)
I've been trying to look for an example but only with one unknown. In my case of studies, I have 4 unknowns. I just want to make sure is it correct the way I'm writing the coding to find the root ...
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0answers
28 views
0
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0answers
36 views
How to prove that this function has a unique root? [migrated]
I want to show that f has always a unique root,
...
1
vote
1answer
47 views
1
vote
2answers
85 views
Computing periodic points of some function
Given a function h[{x_, y_}, b_, c_] := {x^2 + c - b*y, x} for some parameter values b and c ...
2
votes
3answers
85 views
ODE problem using DSolve
I would like to use DSolve (or NDSolve) to verify that the solution to the ODE problem
-4(v''[t]+(2/t)v'[t])-2*v[t]*Log[v[t]]-(3+(3/2)Log[4 Pi])*v[t]==0,
for $t\...
0
votes
1answer
47 views
Solving abstract factorization problem with Mathematica
I'm a Mathematica newbie.
Given something like:
$$(r_0 + r_1 a + r_2 a^2 + r_3 a^5)(r'_0 + r'_1b + r'_2 b^2 + r'_3 b^5) = 1 - a^5 b^5$$
I'd like to determine if there exist $r_i,r'_i$ that solve the ...
1
vote
1answer
87 views
Solving an ordinary differential equation with boundary condition at infinity
I want to solve the following differential equation
f''[z] + (1/z)*f'[z] - f[z] + f[z]^3 == 0
subject to the boundary conditions
$$f^{\prime}(0)=0\qquad\lim_{z\to\...
0
votes
0answers
31 views
can not replace when use ctrl+f
I have a very long output, therefore, I want to find and replace some repeated expressions with abbreviations using crtl +f in Mathematica. when I enter expressions, the mathematical can find it and ...
2
votes
1answer
53 views
Numeric solution of ODEs oscillates strongly and stops halfway？
I tried to reproduce the results of a paper.
The differential equations are given by
...
0
votes
1answer
46 views
NSolve missing solutions
I'm having trouble solving the transcendental equation. For some values of bi, NSolve obtains 6 roots, however when changing the value, it obtains 5. Graphing the function clearly shows that the ...
0
votes
0answers
48 views
Why doesn't Reduce work?
I try to solve an inequality with parameters using Reduce.
The answer i get is :
This system cannot be solved with the methods available to Reduce.
Here is the inequality:
...
0
votes
2answers
76 views
Forcing mathematica to solve polynomials exactly
It used to be the default behavior that Mathematica would solve polynomials of degree 4 exactly. In the current version I have (12.2.2.0) it sometimes gives numerical answers. Is there a way to change ...
3
votes
1answer
63 views
Solve yields complex Root even if the domain is Reals
I want to solve $x^3=a^2$ for $x$ where $a>0$ and $x$ is real. The answer I want is
$$x=a^{2/3}.$$
On Wolfram Cloud, I tried
...
1
vote
1answer
41 views
Numerically obtaining roots as a function of another variable
I have an equation $f(x,y) =0$ that Mathematica can solve numerically using NSolve for a fixed $y$. I want to perform the following operation:
...
0
votes
0answers
32 views
Solve coupled equations in the steady state
I want to solve 16 coupled differential equations in the steady state.
Among the answers, I only require two of the answers. But the Mathematica does not show me the answers in detail!!!
Can anybody ...
0
votes
1answer
62 views
Solve equation system for expression [closed]
How to solve this equations and find specified expression (all integers)?
x * N + y = 2012
y * N + x = 2011
x + y = ?
I've tried but got formulas as an answer ...
