- #1
tracedinair
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Homework Statement
Find the general solution of the following diff. eqn.
y''(t) + 4y'(t) + 4y(t) = t^(-2)*e^(-2t) where t>0
Homework Equations
General soln - Φgeneral(t) + Φparticular(t)
Wronskian - Φ1(t)Φ22'(t) - Φ2(t)Φ1'(t)
The Attempt at a Solution
I'm solving by variation of parameters.
First solving for the general solution, y'' + 4y' + 4y = 0
r2 + 4r + 4 which factors into (r+2)(r+2), so r = -2, -2.
So the gen solution is y = c11e^(-2t) + c2e^(-2t)
Now solving for the particular solution.
Φ1 and Φ2= e^(-2t)
The Wronskian here ends up being 2e^(-4t) - 2e^(-4t) which equals zero.
What went wrong here? I know the Wronskian cannot equal zero here. This is where I am stuck.