All Questions
Tagged with mathematica ordinary-differential-equations
52
questions
0
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1
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81
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Simulation of a pendulum on a spinning Disk
I don't know if this is the right place to ask this Question, but I have previously asked a similar question where i asked how to write a simulation on this phenomenon. I got a great answer with a ...
- 119
1
vote
1
answer
211
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Solution to degenerate case of hypergeometric differential equation
I am trying to find two independent solutions of this differential equation: $$x(1-x)y''(x)+\left[\frac d2-\left(d+\frac12\right)x\right]y'(x)-\frac{(d-1)d}{4}y(x)=0,$$ for $0<x<1$.
This is a ...
- 171
0
votes
1
answer
138
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Partial Differential Equation on a Riemannian Manifold: How to solve complex second order ODE by hand.
I'm working on a project where I discuss using the metric tensor to compute the Laplacian on various Riemannian Manifolds, and how that can aid in solving certain Partial Differential Equations. In ...
0
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53
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Why do these solution graphs not match each other?
Consider the Initial Value Problem, $\frac{dP}{dt} = ((1 + f)^\frac{3}{5} (1 - f)^\frac{2}{5} - 1)P,\ P(0) = 100$, where $f$ is a real parameter between $0$ and $1$, inclusive. Its solution is $P = ...
- 1,922
0
votes
1
answer
624
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How to solve this third order differential equation?
I need help to solve the following differential equation:
$$A^{'''}y + A^{''}(-1 - y\cot{y}) - \frac{2A^{'}}{y} + \frac{2A}{y^{2}}(3+y\cot{y}) = 0$$
where $A$ is a function of $y$ and $A'$ represents ...
1
vote
1
answer
61
views
Solving a differential equation with initial conditions only on the function
I have the initial value problem $\left\{\begin{gather}E_nf_n(x)+f_n''(x) = 0\\
f_n(-a)=f_n(a)=0 \end{gather}\right.$.
Solving it using Laplace transform I get $$f_n(x) = f_0\cos(\sqrt{E_n}x)+\frac{...
- 45
1
vote
3
answers
206
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How to solve this coupled linear ODE
I've tried using mathematica and for some reason it's not working
I think it's a pretty standard problem but for some reason I'm having a hard time
This is essentially a variant of the Rabbi problem I'...
- 101
0
votes
2
answers
90
views
Numerical solution of a linear differential equation with non-constant coefficients
I'm trying to solve the following linear differential equation with non-constant coefficients involving algebraic functions.
$\frac{d \phi}{d t}+\frac{ \left(\Delta ^2 \tau ^2-4 i \tau \sqrt{\Delta ^...
- 121
0
votes
2
answers
177
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General 2nd order ODE with non-constant coefficient
I'm trying to solve the general case of second order ODE: $y''(t) + p(t)y'(t) + q(t)y(t) = 0$.
where $p(t)$ and $q(t)$ are polynomials divides contains some symbolic constant and $t$,$t^2$,$t^3$ and $...
- 13
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0
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187
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How to check on WolframAlpha whether a differential form is exact or closed?
I have $\omega(x, y) = \frac{2xy}{(1+x^2)^2} dx - \frac{1}{1+x^2}dy $. I'd like to check my results, but I don't know how to input the exercise.
I need to check if the differential form is exact, and ...
- 129
1
vote
1
answer
242
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DSolve error, Equation or list of equations expected
pend1[t_] := m x1''[t] + 2 k x1 [t] - k x2[t] == 0;
pend2[t_] := m x2''[t] + 2 k x2[t] - k x1[t] == 0;
iclist = {x1'[0] == 0, x1[0] == 0, x2'[0] == 0, x2[0] == L};
pendlist[t_] = {pend1[t], pend2[t]};...
- 51
1
vote
1
answer
170
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If analytical solvers fail in solving an ODE, does it mean that it is unlikely have an analytical solution?
If analytical solvers (For example, Mathematica and Maple) fail to solve an ODE (Here, I have such situation with the ODE I have given in this question: second order ODE with time-dependent ...
- 161
0
votes
2
answers
470
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Solve ODE for real free falling: $y(x)^2\cdot y^{\prime\prime}(x)]=4\cdot 10^{14}$
I am trying to describe the position of a free falling ball by gravity:
if
$x$ is the time in seconds,
$y$ is the position of the falling ball,
$y^{\prime\prime}(x)$ is its acceleration
then
$$
F=G\...
- 25
2
votes
2
answers
953
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Solve parametric differential equation using Mathematica
Using the method of characteristics on a PDE system, I have gotten a parametric differential equation
$$
\frac{dy}{dx} = \frac{y - xy}{1 + xy - x}.
$$
where $x$ and $y$ are both functions of a third ...
- 259
2
votes
3
answers
191
views
How to solve this differential equation in Mathematica?
I am trying to solve a differential equation in Mathematica:
$$y'' + 2\frac{y'}{x} + (1 - \frac{e^{-x}}{x} - \frac{l(l+1)}{x^2})y = 0$$
I have initial conditions at $x=0$ as:
$$y(0) = a$$
$...
- 430