Linked Questions
21 questions linked to/from Solving an ODE in power series
2
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Finding power series solution for differential equation in Mathematica [duplicate]
I know this topic has been covered before, but I've tried all the solutions I can find from other users' questions and none of them have worked.
I need to find a power series solution to the ...
- 23
2
votes
2
answers
493
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How to get the series coefficient of a function defined by a differential equation [duplicate]
I need a Taylor series approximation for $x(t)$, which is defined by the following differential equation.
$\frac{dx}{dt}=-k_1 x+(1-x)k_2 e^{-k_3 t}$, $x(0)=0$
...
- 283
2
votes
1
answer
332
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Solving for the coefficients of a series [duplicate]
Suppose I have a given series $A(z)=\Sigma a_nz^n$
I want to solve a differential equation for $B(z)$ in terms of coefficients of $a_n$ as a series. Possibly with ansatz $B(z)=\Sigma b_nz^n$ or other ...
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1
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0
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Solving differential equations with sums (power series) [duplicate]
I have sets of 10 differential equations, but for this purpose I'll demonstrate what I need on one example that can be solved by hand.
My equation is this:
$$4GJ\Omega(\theta)\Omega'(\theta)\xi^\...
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-1
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1
answer
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How to find the power series solution of this ordinary differential equation using MMA [duplicate]
I already know that the solution of this differential equation $y''(x) - x*y(x) = 0$ can be expressed by the following power series:
$$y(x)=c0(1+\frac{x^{3}}{2\times3}+\frac{x^{6}}{2\times3\times5\...
9
votes
3
answers
872
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How do I find a series solution for $e^{-\frac{1}{2}f'(x)} \mathrm{cosh}( f(x) ) = ax + b$?
I am trying to approximate a function $f(x)$ satisfying a relation between $f(x)$ and its first derivative. How do I find a series solution for $$e^{-\frac{1}{2}f'(x)} \mathrm{cosh}( f(x) ) = ax + e^{-...
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3
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Solution of equation with power series (perturbation)
So I need to use Mathematica to find the solution of $y=x- \epsilon \sin(2y)$ as a power series in terms of $\epsilon$. I'd assume I'd need to create an equation $f=x-y- \epsilon \sin(2y)$, then ...
- 61
10
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1
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982
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Trouble with shooting method for a 4th-order differential equation
I'm trying to solve the following forth-order ODE with the shooting method:
$$\frac{1}{5}(y-2xy^\prime)=\frac{1}{x}\left\{\frac{xy^\prime}{y}+xy^3
\left[\frac{(xy^\prime)^\prime}{x} \right]^\prime \...
- 491
0
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2
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How to solve the second order differential equation [duplicate]
I've been trying to do code this for a two or so hours, and I can't seem to do it. Please help..
I am trying to solve the following second-order differential equation:
...
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2
votes
2
answers
695
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DSolve not satisfying initial conditions
I am trying to solve the following nonlinear, non-homogeneous, first order ODE:
$y'(t)=\sqrt{y(t)}-B$
$y(0)=B^2$
$B=const$
In code:
...
- 121
1
vote
2
answers
1k
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Solving recursion relation from power series
I am interested in solving differential equations in the form of power series. Let's say we have following equation:
$$f^{\prime \prime} (\rho) + \left( \frac{2 e^{-k \rho}}{\rho} - \varepsilon \...
- 2,396
7
votes
1
answer
691
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Trouble with shooting method for a 4th-order stiff ODE
The ODE I need to solve is
$$\left(y^3y^{\prime\prime\prime}\right)^\prime+\frac{5}{8}xy^\prime-\frac{1}{2}y+\frac{c}{y}=0$$
where $\prime$ denotes differentiation, $c$ is a constant and $0<c\le1$....
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0
votes
0
answers
906
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Solving PDEs using Taylor series
I'm thinking of solving a Partial differential algebraic equation using multidimensional polynomial (i.e. Taylor series). Consider the PDAE:
$$\mathbf F \left( \mathbf x, \mathbf y, \frac{\partial ...
- 615
0
votes
2
answers
407
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Getting the coefficients of a series that solves a differential equations
I have an example from Stewart's Calculus where the equation $y'' + y = 0$ is solved using power series. The equation
...
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0
votes
1
answer
239
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Differentiation of infinite series does not seem to be useful
Trying series solution of differential equations, the routine is to define a function as a series, and differentiate it.
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