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## Homework Statement

Find the general solution.

## Homework Equations

y"+y=x

^{2}sin2x

## The Attempt at a Solution

Characteristic equation would be:

m

^{2}+ 1 = 0

So,m

^{2}= -1

Therefore, m = i or m = -i.

Complementary function would be : Asinx+Bcosx where,A and B are constants respectively.

If I write the particular integral as (Cx

^{2}+Dx+E)sin2x + (Px

^{2}+Qx+R)cos2x

Then,it would be very tedious to solve.

Is there any alternative way like writing sin2x as Imaginary part of e

^{i2x}and then solving the particular integral?