Questions tagged [equation-solving]
Questions on the analytic and numerical equation solving functions of Mathematica (Solve, Reduce, NSolve, FindRoot, DSolve, RSolve, etc.).
5,277
questions
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0answers
48 views
Solving a complicated, non-polynomial dispersion relation
I am quite new to Mathematica, so I apologise if the following question is very basic; I can't seem to find an appropriate answer anywhere!
I am trying to solve a quite complicated dispersion relation ...
2
votes
2answers
189 views
How to visualize a Lagrange problem with Mathematica?
I had asked a question here, which I was advised to open a new question for my further problems.
I have a function as $f(a_1, a_2) = a_1^2 \sigma_1^2 + a_2^2 \sigma_2^2$, which is subjected to the ...
0
votes
1answer
64 views
Is there any possibility to visually examine a Lagrange problem with Mathematica?
I have the function: $f(a_1, a_2) = a_1^2 \sigma_1^2 + a_2^2 \sigma_2^2$, which is subjected to the constraint: $a_1 + a_2 = 1$. I have obtained that: $$a_i = \frac{\sigma_i^{-2}}{\sum_{j = 1}^2 \...
1
vote
1answer
75 views
Rewrite a variable in terms of another variable
I have two variables
t = 1/Sqrt[2] (Sqrt[1 + Cos[a]] + Sqrt[1 - Cos[a]] +
Sqrt[1 + Cos[b]] + Sqrt[1 - Cos[b]] + Sqrt[1 + Cos[c]] +
Sqrt[1 - Cos[c]])
and
<...
1
vote
0answers
64 views
Axes ticks scaled in powers of ten
I'm trying to plot the solution of an ODE and I would like to have the ticks in powers of ten. Although, this happes automatically from Mathematica for small orders, such as ...
6
votes
2answers
659 views
Why does Mathematica not give the simple solution of the given equations?
I want to solve this system of two equations for $x$
$$\{ \sin (2\pi x)+\sin (\frac{2\pi}y)=0 \quad , \quad \cos (2\pi x)-\cos (\frac{2\pi}y)=0 \} \qquad (1)$$
I use ...
0
votes
0answers
52 views
0
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0answers
46 views
Solve set of equations for function [closed]
I have a set of two equations linear in two functions a[r,t] and b[r,t]. However, in these equations other functions like ...
2
votes
2answers
174 views
How can I make sure that there are real roots for the given function? Can I trust the plot only?
I have this function
$$f(x)=(\pi -2 x)^2 \sin \left(\frac{\pi ^2}{2 x-2 \pi }+\frac{1}{2} \csc ^{-1}\left(\frac{4 \pi (\pi -x) \csc \left(\frac{\pi ^2}{x-\pi }\right)}{4 (\pi -x)^2+\pi ^2}\right)\...
3
votes
1answer
215 views
1
vote
1answer
140 views
Why this equation cannot be solved in Mathematica?
I do not understand why the following equation cannot be solved in Mathematica.
Solve[Log[(-Exp[x] + Sqrt[2 - 3*Exp[2*x]])/2] == c*x, x]
The left hand side is ...
-1
votes
0answers
43 views
Defining parametric function resulting from DSolve
I am trying to define a function that is a solution of a simple ODE with a parameter, for example
...
1
vote
1answer
50 views
0
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0answers
47 views
I want to solve 6 equations with three variables. How to solve it? [closed]
I have a 3 \times 3 symmetric matrix equation with 3 variables. Thus, I get 6 different equations of three variables. There is one more variable which can be varied in a given range. How can I solve ...
2
votes
0answers
41 views
Superfluous un-simplifiable condition returned by Reduce
No real "problem" here, just wondering why this is happening and how one might force Mathematica to simplify this. Consider:
...
7
votes
1answer
208 views
Steffensen's Method Implementation in Mathematica
This is sort of a math and Mathematica Language question since I do not know which one is going wrong.
I am trying to implement Steffensen's Method for Nonlinear Systems of Equations and the first ...
6
votes
3answers
472 views
Prove an inequality over the reals, given a constraint
Given $a,b,c \geq 0$ and $$a + b + c = 3$$
prove
$$\frac{a}{b^2 + 1} + \frac{b}{c^2 + 1} + \frac{c}{a^2 + 1} \geq \frac{3}{2}$$
One can prove the above using a great deal of "human" insight ...
1
vote
1answer
131 views
There are some warnings thrown with NDSolve here. How can I change my code to avoid them?
I want to solve some differential equations, but the warnings "NDSolve change the value" are thrown. How do I change the equations?
Are there some equations that are not allowed? Are some ...
1
vote
1answer
131 views
NDsolve to solve Nonlinear Schrödinger or Gross–Pitaevskii Equation?
I am trying to used NDsolve to solve Nonlinear Schroedinger Equation:
...
0
votes
1answer
53 views
How to use Nsolve to tackle a Bessel-related function?
I tried to get the result of the value of ncoeff as the function of wl,codes was pasted blow as well as the picture in MMA,can somebody give me some guidance ,cause my codes take a long time though,it ...
5
votes
1answer
76 views
DSolve inconsistently able to evaluate expression
I am trying to use DSolve to evaluate a coupled system of ODEs as follows
DSolve[{Y0[X] + Y0''[X] == 0, Y1[X] + Y1''[X] == X Y0[X]}, {Y0[X], Y1[X]}, X]
However, ...
1
vote
2answers
48 views
Using NSolve to get a solution for Bessel-related functions
I want to get a solution of a equation using NSolve.
$BesselI[1,x]/(x*BesselI[0,x])=0.2$
So I plugged this equation to NSolve:
...
1
vote
1answer
112 views
Is the following equation solvable by Mathematica? [closed]
I want to solve and plot the solutions of the following equation, where Mathematica is still running and doesn't return anything:
...
0
votes
1answer
42 views
Plot the region given by inequaities
How can one visualize the regions of intersection of the following
...
1
vote
0answers
52 views
FindInstance: How does it work for linear inequalities?
I have a set of linear inequalities, rational coefficients.
When FindInstance returns {}, does that really mean there is no ...
1
vote
0answers
53 views
solving ordinary coupled differential equation
I have a set of 8 ordinary differential equations containing matrices which I need to solve using initial conditions. I have written the equations in this form:
...
-1
votes
0answers
69 views
time evolution in time dependent hamiltonian
I have a time dependent Hamiltonian(A(t)) which NOT commutes at different times.
dU(t)/dt=A(t)U(t)+n(t)
How can I find the time evolution operator of this system so that I can solve it in Mathematica? ...
0
votes
1answer
62 views
Construct a matrix from its elements and solve the eigenvalue problem
I want to construct a 10 by 10 matrix whose elements are given by
$$
H_{nm}=\delta_{nm}\left (n^2+v[b_1-b_0-h(2m,b_0,b_1)]\right) \\ +v(1-\delta_{nm})\left (h(n-m,b_0,b_1)-h(n+m,b_0,b_1)\right)
$$
...
0
votes
1answer
52 views
Stationary Distribution of Markov Chain [closed]
I'm trying to compute the stationary distribution of the following Markov chain:
$$P=\left(
\begin{array}{cc}
p_{11} & p_{12} \\
p_{21} & p_{22} \\
\end{array}
\right)$$
I know you have to ...
0
votes
0answers
38 views
Equation issue: Solve gives an empty output
I need c1,c2....c9 values. Why is Solve returning an empty list?
How i can fix it? Thanks for any advice.
...
0
votes
1answer
65 views
Plotting equation with some unknown parameters
I am new to the Mathematica and I have a question about the plotting. I am trying to plot the transcendental equation
$$\tan{(z)}=\sqrt{\frac{1}{2m_0}\left (\frac{z_0}{z}\right)^2-1}
$$
where the ...
-1
votes
0answers
89 views
Creating An Input That Crushes The Application and/or Computer?
Dear StackExchange Users,
Can anyone assist me in creating a line of input that will malfunction the Wolfram Mathematica 12.3 application (and ideally the computer) when it executes/been executed? In ...
0
votes
1answer
77 views
No solution to the equation even though it has one
I was trying out Mathematica with a simple equation. I tried this one out, but it outputted nothing and when I went on WolframAlpha to test it, there was a result (c = 3 btw). Please let me know if ...
0
votes
1answer
62 views
How to find the integer numbers a, b, c, d, e, m satifying the following conditions?
I know that, the function f[x_] := (x^2 + 6 x + 5)/(x^2 + 2 x + 3) with
D[f[x], x] have two integer solutions ...
3
votes
2answers
170 views
Aren't roots of polynomial equations smooth functions of their parameters?
I am trying to find the solution of cubic equation as a function of $kz$
...
0
votes
0answers
65 views
Plot is fast, solve is slow - what optimizations can be made?
I'm trying to solve a 3D geometric problem in terms of 3 variables (rotational angles), and I think the end is finally in sight - quite literally, I can see on a 3D plot where my solution exists. ...
0
votes
1answer
31 views
finding min S such that integral is greater than some value
I have this function $R(r)$, and $r*R^2$ is a probability density function.
...
0
votes
1answer
62 views
Trouble while trying to re-run open source code
I am a physics student and this is my first time working with Mathematica. I am trying to run the notebook mentioned here, titled "Amplification factors of the superradiant scattering of a ...
1
vote
1answer
64 views
1
vote
1answer
54 views
how we can extract the value of the solution of a PDE in a point x? (NDSolve) [closed]
Please I need your help, I calculate the solution of heat equation using methode of line
This is my code:
...
15
votes
2answers
650 views
Nice cubic polynomials
Let a polynomial with integer coefficients be nice if
this polynomial has distinct integer roots;
its derivative has also integer roots.
For instance
$$p(x)=x(x-9)(x-24),\\
p'(x)=3(x-4)(x-18)$$
is ...
0
votes
1answer
50 views
How to solve differential equation with integrating factor method? [closed]
I need to solve first order differential equation of this type:
$$\dfrac{\partial T_1}{\partial T_0} + a \dfrac{T_1}{T_0} = f (T_0)$$
I know it need to be integrating factor method, but I don`t know ...
1
vote
1answer
45 views
Reducing a sum of two cube roots
I'm trying to verify that this sum of cube roots is equal to 1, using Solve, ToRoots, ...
0
votes
1answer
62 views
1
vote
1answer
83 views
NDSolve of a stiff system of ODE's
I am trying to solve numerically the following set of differential equations
...
0
votes
1answer
27 views
How to resolve problem during summation of functions?
I am trying to find out the output of this basic problem but getting an error. If anyone can resolve this will be helpful.
...
0
votes
1answer
85 views
Unable to solve this differential equation with NDSolve. NIntegrate::inumr error
My code goes as follows:
...
0
votes
1answer
88 views
How to solve this system of equations [closed]
How to solve the following system of equations (If it is possible, I am seeking exact solutions)
...
0
votes
1answer
89 views
Modification of Variable In Parametric Plot 3D
I am plotting a 3D plot of my set of ODEs. The ODEs are as follows:
...
4
votes
3answers
172 views
Simplifying the output to Reduce
I am trying to solve a system of inequalities in Mathematica using Reduce:
...
