698 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 ...
427 views

Changing from Cartesian to polar coordinates in partial differential equation [duplicate]

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 ...
209 views

What is a proper way to express derivatives with respect to a symbol? [duplicate]

Mathematica's default way of representing derivatives is to express them with respect to a function's input slot. But what if I want to use the chain rule? To replace df(x)/dx with df(0.5 y)/dy 0.5, ...
118 views

13k views

How to solve ODE with boundary at infinity

y''[x] - x y[x] == 0 y == AiryAi, y[∞] == 0 The analytic solution to this ODE is the Airy function y[x] == AiryAi[x] if ...
10k views

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 ...
899 views

4k views

Why can't Mathematica integrate this?

Integrate[(x^2 + 2 x + 1 + (3 x + 1) Sqrt[x + Log[x]])/(x Sqrt[x + Log[x]] (x + Sqrt[x + Log[x]])), x] (It just returned integral in symbolic form and did ...
5k views

Replace rule with function? Derivatives don't evaluate

Say I have an expression (call it expr) involving a function, f[x]. I'd like to be able to evaluate that for a particular choice of ...
I don’t know how to impose discontinuous internal boundary conditions (BCs) in NDSolve, so I’ve set up an example problem to illustrate my issue. Consider the simple first-order ODE for $f(z)$ on the ...