# Modeling with DE's

I have a question of show that y=x is one solution of the equation (1+x^2)y''-2xy'+2y=0) this is a question that i need to know for a coming exam. i understand and can do everything until the question gets to v''+(2/x(1+x^2))v'=0

then the question skips to IF =e^integral of (2/x(1+x^2))dx. what does this mean and where does it come from

Hootenanny
Staff Emeritus
Gold Member
I have a question of show that y=x is one solution of the equation (1+x^2)y''-2xy'+2y=0) this is a question that i need to know for a coming exam. i understand and can do everything until the question gets to v''+(2/x(1+x^2))v'=0

then the question skips to IF =e^integral of (2/x(1+x^2))dx. what does this mean and where does it come from
IF is known as the http://en.wikipedia.org/wiki/Integrating_factor" [Broken] as it one technique used to solve ODE's.

Last edited by a moderator:
ok thanks and why is the integrating factor that part of the equation?

Hootenanny
Staff Emeritus
Gold Member
ok thanks and why is the integrating factor that part of the equation?

Do you follow, or does it need more explanation?

HallsofIvy