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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 y

_{1}=cos(x) and y

_{2}=sin(x)

Wronskian(cos(x) sin(x))=1

y

_{p}=-v

_{1}y

_{1}+v

_{2}y

_{2}

v

_{1}'=sin(x)tan(x)

=(sin(x))^2/cos(x)

=(1-(cos(x))^2)/cos(x)

=1/cos(x)-cos(x)

v

_{1}=ln|tan(x)+sec(x)|-sin(x)

v

_{2}'=cos(x)tan(x)

=sin(x)

v

_{2}=-cos(x)

y

_{p}=-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.