Linked Questions
52 questions linked to/from Analogue for Maple's dchange - change of variables in differential expressions
1
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2
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776
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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
...
- 383
3
votes
0
answers
436
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 ...
- 12.7k
0
votes
1
answer
235
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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 = ...
-1
votes
1
answer
239
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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, ...
- 1,857
0
votes
1
answer
82
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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:
$$energy=\frac{1}{2}R_s^{'}[t]^2==\frac{4}{3}G\pi\rho R_s[t]^2$$
...
- 1,521
2
votes
0
answers
68
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Replace variable with other variable containing a constant in differential expression [duplicate]
I have the following differential expression:
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- 2,118
0
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0
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51
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Solving differential equation using substituion [duplicate]
I've been trying to solve an differential equation using substitution.
I have the equation
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- 438
2
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0
answers
34
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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 & - &...
- 215
0
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0
answers
24
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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)-\...
- 221
26
votes
3
answers
14k
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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 ...
- 669
24
votes
4
answers
11k
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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 ...
user1591373
16
votes
4
answers
1k
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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) = ...
- 231k
9
votes
3
answers
5k
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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 ...
- 99
14
votes
4
answers
2k
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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 = ...
- 171
17
votes
2
answers
6k
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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 ...
- 709