Differential equations

**njr008** · October 11th 2008, 11:29 PM

y” + ω^2y =f0 sinΏt

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

**Jhevon** · October 11th 2008, 11:43 PM

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 $y(t) = y_h + y_p$

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