9.16 problem Exercise 22, problem 16, page 240

Internal problem ID [4138]

Book: Ordinary Differential Equations, By Tenenbaum and Pollard. Dover, NY 1963
Section: Chapter 4. Higher order linear differential equations. Lesson 22. Variation of Parameters
Problem number: Exercise 22, problem 16, page 240.
ODE order: 2.
ODE degree: 1.

CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]

Solve \begin {gather*} \boxed {x^{2} y^{\prime \prime }-y^{\prime } x +y-x=0} \end {gather*}

Solution by Maple

Time used: 0.016 (sec). Leaf size: 20

dsolve(x^2*diff(y(x),x$2)-x*diff(y(x),x)+y(x)=x,y(x), singsol=all)
 

\[ y \relax (x ) = c_{2} x +\ln \relax (x ) x c_{1}+\frac {\ln \relax (x )^{2} x}{2} \]

Solution by Mathematica

Time used: 0.013 (sec). Leaf size: 25

DSolve[x^2*y''[x]-x*y'[x]+y[x]==x,y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to \frac {1}{2} x \left (\log ^2(x)+2 c_2 \log (x)+2 c_1\right ) \\ \end{align*}