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776 views

### Symbolic derivatives and substitution [duplicate]

I have troubles substituting functions when I have symbolic derivatives and I need to substitute more symbolic derivatives in my expression. Take for example ...
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I have a partial differential equation: $$\left(x^2+y^2\right)\frac{{{\partial ^2}u(x,y)}}{{\partial {x^2}}} + x^2\frac{{{\partial ^2}u(x,y)}}{{\partial {y^2}}}=0$$ How to change from Cartesian to ...
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### Non-Dimensionalizing PDEs using Mathematica [duplicate]

I am attempting to non-dimensionalize the following equation:  \vec{u}=-(k+k_0)\left[\nabla p -(f'(\phi)-\epsilon^2\nabla^2\phi)\nabla\phi \right]-k_0(1-\phi)\nabla(f'(\phi)-\epsilon^2\nabla^2\phi)-\...
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### How to solve ODE with boundary at infinity

y''[x] - x y[x] == 0 y[0] == AiryAi[0], y[∞] == 0 The analytic solution to this ODE is the Airy function y[x] == AiryAi[x] if ...
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### Change variables in differential expressions

I have a fairly complicated differential expression in terms of a variable r and two unknown functions of r, B[r] and n[r]. I want to do a Taylor expansion of this around r=infinity. I want to do this ...
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