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## Main Question or Discussion Point

**1. Homework Statement**

Given a set of fundamental solutions {e

^{x}*sinx*cosx, e

^{x}*cos(2x)}

**2. Homework Equations**

y''+p(x)y'+q(x)=0

det W(y

_{1},y

_{2}) =Ce

^{-∫p(x)dx}

**3. The Attempt at a Solution**

I took the determinant of the matrix to get

e

^{2x}[cos(2x)cosxsinx-2sin(2x)sinxcosx-cos(2x)sinxcosx- cos

^{2}xcos(2x)+sin

^{2}xcos(2x)

Then using the identities sin

^{2}x+cos

^{2}x = 1 (for the last 2 terms) and sin(2x) = 2sinx*cosx (for the second term) and cancelling the 2 "cos(2x)cosxsinx" (first and third terms) I got

-e

^{2x}(sin

^{2}x+cos(2x))

Setting this equal to Ce

^{-∫p(x)dx}and trying to solve I got as far as

ln(-e

^{2x}(sin

^{2}x+cos(2x))

**/C**) = -∫p(x)dx

and now I'm a little bit stuck, I also don't know how to solve for q(x) here. Thanks for the help!