# Questions tagged [differential-equations]

Questions on the symbolic (DSolve, DifferentialRoot) and numerical (NDSolve) solutions of differential equations in Mathematica.

3,826 questions
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### How can solve this partial differential equation (PDE) and plot?

How can plot and solve this partial differential equation in mathematica? $$K \frac{\partial^2 T}{\partial x^2}- h (T-T_m) = \frac{\partial T}{\partial t}$$ $Tm = 25$ $k= 47$ $h= 1.5$ ...
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### How to plot Implicit function Exp^(-ArcTan[y/x]) * Sqrt[x^2 + y^2]==C , for example, C -> Range[-12, 12]?

I tried many functions to plot implicit function: Exp[-ArcTan[y/x]] * Sqrt[x^2 + y^2]==C Does anyone have an idea how to do that ? (This is General Integral of ...
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### Why can't DSolve solve this simple system of PDEs?

I have a system of two PDEs: $$\frac{\partial\psi}{\partial y}=ax+b$$ $$-\frac{\partial\psi}{\partial x}=-ay+cx$$ where $a$, $b$, and $c$ are constant reals. When I plug the system into ...
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### Any idea? why NDSolve is very slow for a very small digraph

I have developed (of course with a lot of help from experts in this forum) the following code to speed up the calculations for large digraphs. However, I ended up ...
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### Driving a system of differential equations with an AR1-Process

I have the following system of differential equations: ...
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### Solve PDEs with finite difference scheme by modifying NDSolve-based solver

Motivation As discussed here, NDSolve uses different difference orders for various spatial derivatives and the implicit design could cause trouble in certain cases....
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