8.1.2.72 Second order differential equations

Problem: Find the general solution of the linear homogeneous equation by the given particular solution \( y_{1} \) corresponding to the linear homogeneous equation: \[ y^{\prime \prime}-2(\tan x+1) y^{\prime}+(2 \tan x+1) y=2 e^{x} \sec ^{4} x, y_{1}=e^{x} . \] clip2net.com