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## Homework Statement

let f(t) = t if 0<t<1

1 if 1<t

y" +4y = f(t)

y(0)=0 and y'(0)=0

## Homework Equations

## The Attempt at a Solution

I took g(t)= t(u)t+(1-t)u(t-1)

so then I got

(1/s^2)+e^-2s((-1/s^2)+(2/s))

which goes to

(1/(1-e^-2s))((1-e^-2s-2se^-2s)/s^2)

now I think

Y=L{y(t)}(s)

L{y'}=sY

L{y"}=s^2Y

so (s^2)Y+4Y f(t)

Y(s^2 + 4)=f(t)

so

Y(s^2 + 4)=(1/(1-e^-2s))((1-e^-2s-2se^-2s)/s^2)

Now what do I do from here? If I solve for Y I get

Y=(1/(1-e^-2s))((1-e^-2s-2se^-2s)/s^2)(1/(s^2 +4)

but now what?