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Intial value problem

  • Thread starter Karmel
  • Start date
  • #1
12
0

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?
 

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