7 votes
Accepted

Symbolic solution for steady-state heat equation i.e. Laplace equation inside cylinder

This post contains several code blocks, you can copy them easily with the help of functions here. It's not too surprising to see DSolve failing on the problem, ...
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  • 52.8k
6 votes
Accepted

How to achieve the transformation using DSolveChangeVariables introduced in Mathematica 13.1?

The problem can be solved with new-in-13.1 DSolveChangeVariables of course. If you read the document carefully, you'll notice the correct syntax should be ...
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  • 52.8k
6 votes

Analogue for Maple's dchange - change of variables in differential expressions

2022 Update: Included in Mathematica 13.1 As pointed out by xzczd in his question update, seven years later, finally Mathematica 13.1 introduced the new function DSolveChangeVariables which ...
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  • 414
5 votes
Accepted

Equating coefficients of two expressions

Another way with SolveAlways ...
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  • 15.7k
5 votes

Small question about the output form of the derivative

Clear["Global`*"] Use HoldForm ...
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  • 121k
5 votes

How do I implement convolution integrals symbolically (not numerically)?

On second thought, I don't think your approach to calculating the convolution is mathematically sound. The Wiki page, and the MathWorld page it references, both state that "the integral of a ...
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4 votes

ComplexExpand no longer assumes Derivative[__][__][__] as real

Here another workaround that may be safe (as it would likely affect only expressions containing u'): ...
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  • 216k
4 votes

ComplexExpand no longer assumes Derivative[__][__][__] as real

Comments have identified this as a bug; in the meantime, a simple way to bring back the old behavior for ComplexExpand in a given session can be obtained by adding ...
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  • 8,208
4 votes

How do I implement convolution integrals symbolically (not numerically)?

s1[t_] := UnitBox[t - 0.5]; s2[t_] := SawtoothWave[t] UnitBox[t - 0.5] res = Convolve[s1[s], s2[s], s, t] $$\begin{array}{cc} \{ & \begin{array}{cc} 0.5 t^2 ...
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  • 16.2k
4 votes

Equating coefficients of two expressions

To be able to use "CoefficientList" we must first transform your equation to a polynomial by e.g. Lefthand Side-Righthand Side. Then we replace Cos[i theta] by e.g. c^i: ...
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3 votes

Equating coefficients of two expressions

Here's a way that's a bit silly but which should work. (I'm on a computer without MM on it right now, so if the code doesn't work please ping me in the comments and I'll fix it as soon as I'm able.) <...
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1 vote

Loop over multiple variables with readable code

(I'm repeating some things I said in a comment just for the sake of completeness :) ) Welcome! In general, you shouldn't use For loops in mathematica, especially ...
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  • 8,208
1 vote

RSolve with integer and boolean variable

With the boundary conditions omitted, as permitted by @black, RSolve can solve this problem. ...
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