If varphi(x)=x is a solution of the ordinary differential equation (ODE) d^2y/dx^2-(frac2x^2+frac1x)(xdy/dx-y)=0,quad 0<x<infty, then the general solution of the ODE is given by

Q41Section B (Part B)41 of 120

General solution given one solution

If $\varphi(x)=x$ is a solution of the ordinary differential equation (ODE)

$\frac{d^2y}{dx^2}-\Big(\frac2{x^2}+\frac1x\Big)\Big(x\frac{dy}{dx}-y\Big)=0,\quad 0<x<\infty,$

then the general solution of the ODE is given by

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