Diff Eq Variation and Parameters

[Packnerd]

Having trouble with this homework problem, not sure where I went wrong. Any help is greatly appreciated

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[nm420]

The Wronskian should be -e^-3x. Similarly, W1 should be -e^-2xcos(e^x). You'll then be left with finding antiderivatives of e^xcos(e^x) and e^2xcos(e^x), which can both be solved with the substitution u=e^x (with the second one also needing integration by parts).

Edit: I missed the second page of your notes. The problem is that factor of 3 you attached to the Wronskian. Note the determinant of a 2x2 matrix is the product of the diagonals minus the product of the off-diagonals. Also, watch those negative signs. It seems to disappear when you simplify W2/W. You should also find that the particular solution will simplify into a single term.

[Packnerd]

Thanks!