Questions on the analytic and numeric equation solving functions of Mathematica (Solve, Reduce, NSolve, FindRoot, DSolve, RSolve, etc.).

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4
votes
3answers
212 views

Solving equation

How can I solve this equation: ((a^2 - 1)*((a^2 - 1)*ArcTanh[a] - a))/(2*Sqrt[2*(a^2 - 1)^4]) == C*x I am looking a solution for $a$ in function of $x$. I tried <...
2
votes
1answer
106 views

Maximize a variable in NSolve Function

I want to solve a set of trigometric coupled equations with the NSolve funcion while at the same time trying to maximize a variable which has to be real and between ...
3
votes
3answers
184 views

Cantor Pairing Function

I'm inspecting the Cantor pairing function, that we can find on this link here. But the strange thing is that Mathematica is outputting a wrong result to me. The code below shows the strange behavior....
0
votes
0answers
39 views

Using previous outputs and equations for 3d plots

I am extremely new to Mathematica, and am trying to obtain some plots for my research work. I need to find the roots of a polynomial, and using the roots individually, I need to obtain another ...
1
vote
0answers
48 views

Working of ForAll

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0
votes
0answers
39 views
0
votes
0answers
42 views

Hash in Eigenvalue calculation [duplicate]

When I tried to find the eigenvalue of a 5x5 matrix, I get the following ...
2
votes
1answer
122 views

Differential Equation with Numerically Integrated Boundary Conditions

I have a second order differential equation that I'd like to solve numerically, and then integrate its solution twice to get the parametric equations of a curve. The ODE is: $2 \kappa''(s)+\kappa^3(s)...
0
votes
0answers
94 views

Impose a boundary condition to a function

Background I am trying to impose a boundary condition on a function of two variables $u(x_1,x_2)$. The boundary condition is: $u(x_1,0)=A\cos(\omega x_1)$. The same function in mathematica $u(x_1,0)$...
0
votes
0answers
47 views

Solve huge system of inequalities

I need to solve the huge system of algebraic linear inequalities (up to milions). But the built-in methods like Solve, Reduce, FindInstance... seems to be very slow. I have problem to solve "only" 100 ...
1
vote
4answers
372 views

Equation for the line of intersection between two planes

I have two equations: 2x + y + z = 1 3x - 2y - z = 5 And I have calculated the answers on paper, which gave me $x = 1 + t$, $y = -1 + 5t$ and $z = -7t$. So my ...
0
votes
0answers
35 views

Solvability of a system of equations and inequalities

I want to know if a given system of equalities and inequalities is solvable or not. I do not need the solution, rather just about its solvability. I tried a few variations, but I believe that it can ...
0
votes
2answers
99 views

Solving recursion relation from power series

I am interested in solving differential equations in the form of power series. Let's say we have following equation: $$f^{\prime \prime} (\rho) + \left( \frac{2 e^{-k \rho}}{\rho} - \varepsilon \...
1
vote
1answer
115 views
0
votes
1answer
74 views

norm squared of imaginary function with unknown constants

Is it possible to evaluate the norm squared and expand a given function similar to this, $$ c(t)=\frac{-e^{-iat}}{2}-\bigg[\big(\frac{a-\sqrt{a^2+16b^2}}{4\sqrt{a^2+16b^2}}\big)e^{-\frac{i}{2}(a-\sqrt{...
1
vote
2answers
70 views

Finding roots of a function that includes Bessel functions [duplicate]

I'm fairly new to Mathematica so forgive any stupid mistakes. Here's my function: ...
1
vote
1answer
45 views

Select positive solution based on value of parameter

I want to select positive solutions to Solve[], but as the sign of the solutions depend on the value of some parameters/other variable, I am not sure how to do this?...
1
vote
1answer
67 views

Differential equation [closed]

How does one solve this differential equation? $$y' = \frac{x^3 + 2x^2 y - y^3}{x^3 + x^2 y}$$
0
votes
1answer
61 views

Solve homogeneous system [closed]

Let x^2*y + x^2*z + x*y^2 + y^2*z + xz^2 + yz^2+ xyz =0 x^3-xyz + x^2*y-xyz + x^2*z-xyz + xy^2-xyz - xy*z+y^2*z - xyz+xz^2 - xyz+yz^2 =0 x^3+3*xyz+7*yz^2 + xy*z+y^3+9*y*z^2 + x^2*y+6*xyz+4*y*z^2 ...
1
vote
2answers
86 views

Solutions to Non-linear equation system

I have been trying to solve the following system of equations: ...
1
vote
1answer
60 views

System of polynomial equations with Solve does not converge

The Exp-method [1] is an analytical solution method for differential equations. Essentially, the method boils down to the solution of a system of nonlinear polynomial algebraic equations. In [1] (and ...
0
votes
0answers
34 views

Why differential equation reduces? [duplicate]

I am trying to ND-Solve the following equation: eqns = {x''[t] == -x[t], x'[0] == 0, x[0] == 4} The problem, is when I enter it, Mathematica reduces it to <...
1
vote
1answer
60 views

Precision in calculation [duplicate]

I am writing some code to demonstrate the effect of the number of significant figures a coefficient has on the solution of a nonlinear equation. I define the coefficient as follows: ...
0
votes
1answer
90 views

NDSolve for a system of nonlinear coupled pde

I try to solve a system($n$) of coupled nonlinear 1-d PDE's which is basically coupled sine-Gordon equations (through 2nd spatial derivative) in time and space. I am interested in the dynamics when I ...
0
votes
1answer
101 views

Find partial solution for underdetermined system of Boolean equations (Minesweeper)

In this article about creating a Minesweeper solver, the author talks about using matrices to solve given portions of a Minesweeper board. While reading that, I thought of a different way to limit the ...
2
votes
0answers
65 views

Estimating processing time for commands

I am trying to evaluate some equations by using Taylor series of expansion (Series[], ExpandAll[], and Normal[] command), and using n equation and n unknown (Solve). Following is not full command (if ...
0
votes
1answer
50 views

Symbolic Maximization: does not work with symbolic power?

Simple question from a beginner: I seem to be unable to do maximization if the variable has a power specified symbolically instead of numerically? ...
2
votes
1answer
48 views

Passing a list to a nested vector function

In order to apply a newton-rhapson algorithm to solve a set of nonlinear vector equations such as these, f[x_, y_] = {x^2 - 3*y + 6, (y + 1)^2 - x - 33} I need ...
-1
votes
1answer
67 views

How can I solve a certain statics problem [closed]

Does someone have any idea how to solve it or from where to start?
0
votes
1answer
86 views

Solve non-linear system of 16 equations [closed]

I need a solution to a non-linear system of 16 equations, I am trying the following command and nothing is happening: ...
3
votes
3answers
191 views

Determine integer results using Solve

I'm trying to solve a Pythagorean pairs for m and n (for m and n < 100) which give integer p values in the following equation: Sqrt[m^2 + n^2] == p I may ...
0
votes
1answer
122 views

NSolve takes too long time!

I am trying to solve the following problem numerically and I faced two things: 1- It takes too long time to give solutions. 2- there are many roots for the equation but NSolve doesn't give all thee ...
5
votes
1answer
111 views

SystemException[“MemoryAllocationFailure”] Uncaught SystemException returned to top level from NSolve

Bug introduced in 10.0.0 When trying to solve 8 equations in 8 unknowns, I get SystemException["MemoryAllocationFailure"]. I am not sure if I am doing something ...
1
vote
1answer
101 views

Different interpretation of system of equations

Given the variables ...
1
vote
2answers
62 views

Solving simple transcendental equation [duplicate]

I would like to solve Tan[x] == 1/x Solve[] does not work, suggesting that there is no nice analytical solution for x. Surprisingly, NSolve[] does not work ...
1
vote
1answer
64 views

Is this expression solvable and if so is there a better way to do it?

I would like to solve this polynomial of third order for its roots: ...
0
votes
0answers
36 views

Solving an inequality with Root objects

Given q1 = Root[(48 a^2 + 16 b) #^4 - (40 a^3 + 168 a b)#^3 + (-45 a^4 + 225 a^2 b + 72 b^2) #^2 + (27a^3 b - 162 a b^2) # + 27 b^3 &,1] Now, I know that the ...
1
vote
2answers
66 views

Mathematica shows complex roots while asked for reals?

I ran the following code in Mathematica ToRadicals[Reduce[-14848 c^4 + 38016 c^3 x - 30888 c^2 x^2 + 6480 c x^3 + 1215 x^4 == 0 && c < 0,x,Reals]] ...
0
votes
0answers
32 views

Different root objects

Consider the quartic polynomial $$(48a^2+16b)x^4-(40a^3+168 ab)x^3+(-45 a^4+225a^2 b+ 72b^2)x^2+(27a^3 b - 162 ab^2)x+27b^3, \qquad (*)$$ where $a<0$. Consider ...
-1
votes
1answer
34 views

How can I get all the possible solutions using NSolve [closed]

How can I get all the possible solutions using NSolve. The following equation has eight analytic solutions. These analytic solutions are obtain using "Solve" as ...
0
votes
0answers
17 views
1
vote
0answers
48 views

List within a Do loop, I can't get any values [duplicate]

I am having the following problem. I am trying to get some values from solving an equation and apply them into a list but in the output I get nothing but the symbol of the variable... The code is as ...
6
votes
2answers
159 views

NDSolve and matrix formulation do not produce the same result. Why and which is more precise?

Let's assume a vector of variables $\vec a=(a_1(t),a_2(t),a_3(t))$ and let's assume a following DE$$C\ddot{\vec a}=B\dot{\vec a}+A\vec{a}+\vec F.$$ If $A$ and $C$ are both reversible, than the DE can ...
0
votes
1answer
86 views

problem in solving equation

this happened to me when I try to get (f) which should equal sqrt(3)/2 is there any problem in my formula or what? ...
1
vote
0answers
95 views

Need help solving a polynomial system [closed]

I need help solving the following system of equations: ...
0
votes
0answers
40 views

NSolve with a term that is an interpolating function

I need to solve this system of equations Log[np[x]] + psi[x] + f[np[x], nm[x]] == 0 Log[nm[x]] - psi[x] + f[np[x], nm[x]] == 0 For ...
2
votes
0answers
52 views

Unusual error message from Solve when called by DSolve

Question 111150 presents an equation nonlinear in its leading derivative ...
1
vote
1answer
42 views

How to solve from a list

I have this equation: $y(t)=aE^{-bE^{-ct}}$ and I have this list: ...
1
vote
1answer
48 views

Maclaurin Series - Table

I'm starting to learn Mathematica. I have to solved this eq and draw the graph. It is developing a series of Taylor in about x0 == 0. This is my equation to solve ...
0
votes
1answer
82 views

Maclaurin series [closed]

Can someone tells me, why is that not working? I'm starting to learn Mathematica. I have to solved this eq and draw the graph. It is developing a series of Taylor in about x0 = 0. ...