# 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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### 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 ...
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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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### 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 "...
54 views

### 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 ...
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1 vote
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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 ...
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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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### 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 ...
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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. ...
233 views

### 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.... 85 views

### 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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### 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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