8.1.3.22 Higher order differential equations

Problem: Checking that the functions \( y_{1}(x)=\cos x \) and \( y_{2}(x)= \) \( =x \cos x \) form a fundamental system of solutions of the equation \( y^{\prime \prime}+2 \tan x \cdot y^{\prime}+\left(2 \tan ^{2} x+1\right) y=0 \), find the general solution of the equation \( \cot x \cdot y^{\prime \prime}+2 y^{\prime}+(2 \tan x+\cot x) y=\cos ^{2} x \). clip2net.com