
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:
\[
y^{\prime \prime}-2(\tan x+1) y^{\prime}+(2 \tan x+1) y=2 e^{x} \sec ^{4} x, y_{1}=e^{x} .
\]
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