(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

I understand how to do initial value problems but I'm slightly stuck when the initial values are y(0) = y'(0)=0

The question is Solve:

y''+3y''+2y=f(t), y(0)=y'(0)=0 where f(t) is a square wave.

2. Relevant equations

[itex]\Im[/itex]{y'} =s[itex]\Im[/itex]{y}-y(0)

[itex]\Im[/itex]{y''}=s[itex]^{2}[/itex][itex]\Im[/itex]-sy'(0)-y'(0)

3. The attempt at a solution

I've gotten so far:

(s[itex]^{2}[/itex][itex]\Im[/itex](y)-sy(0)-y'(0))+3(s[itex]\Im[/itex](y)-y(0))+2[itex]\Im[/itex](y)=F(t)

[itex]\Rightarrow[/itex] (s[itex]^{2}[/itex]-y'(0)-0)+3s-y'(0)+2=F(t)

Its then when I substitute in the initial condition I get

s[itex]^{2}[/itex]+3s+2=F(t)

I'm not sure this is right because I cant then do partial fractions or the inverse of it to get the final answer.

The other thing is I dont understand how F(t) being a square wave affects it.

Any help would be greatly appreciated!

1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution

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# Homework Help: Initial value problem and laplace transform

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