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Differential Equations : Variation of Parameters

Determine the particular solution for the following nonhomogeneous differential equation using the method of variation of parameters
Y" + y =tan(x); 0< x < pi/2

I got characteristic equation as y = U1 sin(x) + U2 cos (x)
I was able to get thru to set the original D.E. to u'1 (x) cos (x) - u'2 (x) sin (x) = tan (x)

Original D.E. had u'1(x) sin(x) + u'2(x) cos (x) = 0. And book explained to solve of U'2(x) and go from there. This is where my problems began! Help

Book has answer as y = c1 cosx + c2 sinx -(cosx)ln(tanx + secx)

Solution Summary

A variation of parameters problem is solved. The solution is detailed and well presented. The response received a rating of "5/5" from the student who originally posted the question.