Answer:y=
Acosx+Bsinx +cosx ln(cosx)+x sinx
Explanation:
given equation y''+y=secx
auxiliary equation

so CF is y=Acosx+Bsinx
now

using wronskian formula

=

now f(x)=secx




now particular integrals are
PI=cosx ln(cosx)+x sinx
total solution
y= C.F+P.I
y=Acosx+Bsinx +cosx ln(cosx)+x sinx