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

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

1 if 1<t

y" +4y = f(t)

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

2. Relevant equations

3. 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?

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: Intial value problem

Can you offer guidance or do you also need help?

Draft saved
Draft deleted

**Physics Forums | Science Articles, Homework Help, Discussion**