- #1
ElijahRockers
Gold Member
- 270
- 10
Homework Statement
Solve
y'' + y = f(t), y(0)=0, y'(0)=1,
f(t)=
(0 for 0<t<pi)
(1 for pi<t<2pi)
(0 for t>2pi)
The Attempt at a Solution
y'' + y = upi(t)-u2pi(t)
s2L{y} -sy(0) -y'(0) +L{y} = L{upi(t)} -Lu2pi(t)}
L{y}(s2+1) -1 = (e-pi*s/s) -(e-2pi*s/s)
L{y} = (e-pi*s/s(s2+1)) -(e-2pi*s/s(s2+1)) +1/(s2+1)
This is where I get stuck... I'm assuming that I can factor out the e terms separately, then use decomposition of partial fractions to separate 1/s(s2+1), but when I do that I get meaningless values for A and B.
1/s(s2+1) = A/s + B/s2+1
1= A(s2+1) +Bs
1 = As2 +Bs +A
From that I can infer that A = 1, but also that A=0, and B=0.
What am I doing wrong?