- #1
osheari1
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Homework Statement
Find a particular solution y_c to the complex differential equation
y'' + 2 y' + 3 y = -1 exp(2 i t)
y_c=
Using the solution y_c, construct a particular solution y_{1p} to the following differential equation
y'' + 2 y' + 3 y = -1 sin(2 t)
y_{1p} =
Again using the solution y_c, construct a particular solution y_{2p} to the following differential equation
y'' + 2 y' + 3 y = -1 cos(2 t)
y_{2p} =
Homework Equations
y = Ae^(2it)
The Attempt at a Solution
I let y'' + 2y' + 3y = 0 and then solve getting
e^(-t)(cos(sqrt2t) + sin(sqrt2t)) + g(h)
then solve for the g(h) by first finding A
y = Ae^(2it), y' = A2ie^(2it), y'' = -A4e^(2it)
substitute and solve for A getting -1/(4i - 1)
→ y(t) = e^(-t)(cos(sqrt2t) + sin(sqrt2t)) -1/(4i-1)e^(2it)
the Constants of integration can be anything for this problem so i just let them equal 1
but this is still not the right answer
please help