Ordinary Differential Equations............variations of parameters...

[BamBam215]

So I understand how to use the method of variation of parameters when the coefficients are constants. But when they are functions, I don't know what to do? My book doesn't show how to do it either. Anyone happen to know?

 

[TwiceOver]

huh?

EDIT: We need a mathematics subforum.

 

[chuckywang]

oh man, it's too much typing....

try this link: http://www.sosmath.com/diffeq/...riation/variation.html

 

[BamBam215]

i know how to solve it when the diff equation is something like y'' + 4y' +4 = e^5t (where the constants are coefficients).
what i don't know is how to solve it when the diff equation is something like y'' + (1/2-x^2)y' + (x^3+3) = e^5t (where the constants are functions, not coefficients).

 

[chuckywang]

read the link....it does the case when the coeff. are functions.

 

[BamBam215]

the link only gives an example of a case where the coefficients are constants. in order to use the variation of parameters, you first need to solve for the homogenous equation. in every example i've seen, it starts off with a 2nd order diff equation that has constant coefficients and it's easy to find the solution to the homogenous solution. but i have yet to find one where the 2nd order diff equation has functions as the coefficients.

 

[ActuaryTm]

Integrate x^(-2) to find the answer.