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

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} =

2. Relevant equations

y = Ae^(2it)

3. 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

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# Particular Solutions of Undetermined Coefficients

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