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Homework Statement
A particular solution of y'' + 4y = tanx
Answer choices are:
(a) 1/2*cos(2x)ln|sec(2x)+tan(2x)|
(b) -1/2*cos(2x)ln|sec(2x)+tan(2x)|
(c) 1/2*sin(2x)(ln*cos(x)+x*sec(2x))
(d) 1/2*sin(2x)(ln*cos(x)-x*sec(2x))
(e) none of the above
Homework Equations
The Attempt at a Solution
I used variation of parameters with y1=cos(x) and y2=sin(x)
Wronskian(cos(x) sin(x))=1
yp=-v1y1+v2y2
v1'=sin(x)tan(x)
=(sin(x))^2/cos(x)
=(1-(cos(x))^2)/cos(x)
=1/cos(x)-cos(x)
v1=ln|tan(x)+sec(x)|-sin(x)
v2'=cos(x)tan(x)
=sin(x)
v2=-cos(x)
yp=-cos(x)(ln|tan(x)+sec(x)|-sin(x))+sin(x)(-cos(x))
=-cos(x)ln|tan(x)+sec(x)|+cos(x)sin(x)-sin(x)cos(x)
=-cos(x)ln|tan(x)+sec(x)|
Given the answer choices, now I feel like I've missed something fundamental. It's probably obvious. So sorry.