# Differential equations

• Oct 12th 2008, 12:29 AM
njr008
Differential equations
y” + ω^2y =f0 sinΏt

The end part has really confused me and I would like some help please.
• Oct 12th 2008, 12:43 AM
Jhevon
Quote:

Originally Posted by njr008
y” + ω^2y =f0 sinΏt

The end part has really confused me and I would like some help please.

first solve the homogeneous equation, $y'' + \omega^2 y = 0$ by assuming a solution $y_h = e^{rt}$

then, let $y_p = A \sin \Omega t + B \cos \Omega t$

find $y_p''$ and plug it into the original differential equation and solve for $A$ and $B$ by equating coefficients

your final solution is $y(t) = y_h + y_p$