8.1.3.21 Higher order differential equations

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