solving second order non-homogeneous differential equation 3 Help me to solve this  non-homogeneous differential equation :
$
y''+y=\tan x
$
$
0<x<\dfrac{\pi}{2}
$
I could reach to $y_{c}=c_{1}\cos x + c_{2}\sin x$ but particular solution is where I stopped.

Knowing a solution of the homogeneous ODE, for example $c\cos(x)$, remplace the constant $c$ by a function $Y(x)$ , i.e.: change of function $y=Y(x)\cos(x)$. This allows to reduce the second order ODE to a first order ODE easier to solve.

