Linked Questions

1
vote
2answers
607 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 ...
3
votes
0answers
400 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 ...
-1
votes
1answer
186 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, ...
0
votes
1answer
65 views

How do I make a substitution to an expression inside a derivative? [duplicate]

Pardon if I didn't ask the question correctly. Still trying to figure out the language. I have the following expression: $$energy=\frac{1}{2}R_s^{'}[t]^2==\frac{4}{3}G\pi\rho R_s[t]^2$$ ...
0
votes
1answer
71 views

Changing variables to obtain derivatives of new variables [duplicate]

Let's say that I have some symbolic expression of a function $x(t)$, and would like to obtain its derivative $x'(t)$. However, I also have the following two identities, $\xi = \omega t$, and $\eta = ...
2
votes
0answers
60 views

Replace variable with other variable containing a constant in differential expression [duplicate]

I have the following differential expression: ...
2
votes
0answers
30 views

Replacement of independent variables in the differential equations with partial derivatives [duplicate]

For example: $\frac{\partial^2 u}{\partial x^2}+4\frac{\partial^2 u}{\partial x \partial y} + 3\frac{\partial^2 u}{\partial y^2}=0$ Replacement: $\left\{\begin{matrix}\xi & = & y & - &...
24
votes
3answers
12k views

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 ...
22
votes
4answers
9k 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 ...
16
votes
4answers
732 views

How to model diffusion through a membrane?

This is a follow-up on How to handle discontinuity in diffusion coefficient? Consider diffusion of $u(t,x)$ on the domain $x \in [0,2]$ with some simple boundary conditions such as $u(0) = 2, u(2) = ...
14
votes
4answers
1k views

Analytic solution to Newtonian gravity differential equation

I was told that I could obtain an analytic solution to a particle falling under the influence of Newtonian gravity by using DSolveValue. What I am given $G = M = ...
7
votes
3answers
3k 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 ...
13
votes
2answers
4k 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 ...
11
votes
2answers
2k views

PDE with Stefan Conditions, a.k.a variable boundary

I want to solve the one-dimensional one-phase Stefan problem, but I don't know how to make Mathematica understand the conditions. If you are not familiar with what I'm asking please refer to this ...
12
votes
2answers
787 views

How to use NDSolve with discontinuities at internal boundaries?

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 ...

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