ODE Method of Variation of Parameters help

**fizzle45** · March 31st 2011, 06:56 PM

Above is my problem sorry that it's a link but It was to hard to convert from latex into here (i used some packages)

**Danny** · April 1st 2011, 04:58 AM

You're missing a term in your variation of parameters formula. Given an nth order linear ODE

$a_n(x)y^{(n)} + a_{n-1}(x)y^{(n-1)} + \cdots + a_1(x)y' + a_0(x)y = f(x)$

with independent solutions $y_1, \cdots , y_n$ the variation of parameters formula is

$\displaystyle y_p = \sum_{k=1}^n y_k \int \dfrac{W_k}{W} \dfrac{f(x)}{a_n(x)}dx$ .

With what you have you set $a_n = 1$ where it should be $a_n = x^3$ . With this assignment things work out giving you the desired $y_p$ .

Thread: ODE Method of Variation of Parameters help

LinkBack

Thread Tools

Display

ODE Method of Variation of Parameters help

Similar Math Help Forum Discussions

Theoretical question on the Variation of Parameters method

Solving using the IF method and variation of parameters

method of variation of parameters to find particular solution of this simple diff eqn

Method of variation of parameters

Solve using method of variation of parameters

Search Tags