What is Series solution: Definition and 110 Discussions
In mathematics, the power series method is used to seek a power series solution to certain differential equations. In general, such a solution assumes a power series with unknown coefficients, then substitutes that solution into the differential equation to find a recurrence relation for the coefficients.
Hi,
I have a system of three coupled nonlinear ODEs:
\frac{d}{du}(nu)=exp(-\phi),
u\frac{du}{dx}=\frac{d\phi}{dx}-\frac{u}{n}exp(-\phi),
\frac{d^2 \phi}{dx^2}=n-exp(-\phi),
with boundary conditions
\phi=\phi'=u=n=0 \text{ at } x=0
Does anyone know, or have references...
Ok I'm giving these another go. I found the following DE from a reduction of order problem and figured that it would be an alright question if I turned it into one requiring a series solution. However I'm stuck. I think it's just a matter of index shifts to get an appropriate recurrence relation...
Im given y"-xy'-y=0 at x0=1.
The problem asks for recurrene relation, and the first four terms in each of two linearly independant solutions, and the general term in each solution.
Whats thrwoing me off is the x0=1. I tried doing y= SUM an(x-1)^n, but when i differenetiate and plug in, i get...
Q1 :For example
Solve the D.E : U''-2xU' +2u = 0
Do I write out the series solution or write somthing like : C1e^r1 + c2e^r2 ,for r1&r2 are the roots of the equation~ What is the different between these two answer?
One more question,
Q2 : Show function (arcsin x )^2 satisfies...
Here's our equation:
\frac{d^2\psi}{du^2}+(\frac{\beta}{\alpha}-u^2)\psi=0
This is the SE for the simple harmonic oscillator. My text goes through an elaborate solution to this DE and ends up resorting to a power series solution, not for psi, but for H, where \psi=H(u)e^{-u^2/2}. The text...
Hi, I'm trying to solve a differential equation and I'm supposed to obtain a recursion formula for the coefficients of the power series solution of the following equation:
w'' + (1/(1+z^2)) w = 0.
The term 1/(1+z^2) I recognize as a geometric series and can be expressed as sum of 0 to...
Problem
y^{\prime} = x^2 y
General Comments
There must be some kind of flaw in my solution as I don't get to the same result as the one my book provides:
y = c_0 \sum _{n=0} ^{\infty} \frac{x^{3n}}{3^n n!} = c_0 e^{x^3 / 3} \qquad \fbox{CORRECT ANSWER}
Any help is highly...
I am trying to find the power series solution of
y' = x^2y
but don't know how to arrive at the answer of y = a_0exp(x^3/3). [I know that it's an easily solved separable equation, I'm just trying to figure out how to find the power series solution]
My solution so far:
Assume
y...
I've done a power series solution to a differential equation and got the recursive formula for the coefficients below. Now I am to evaluate it for large j and I don't get the answer in the book.
I'm not sure what method they are using to get the answer although their answer makes sense...