Internal problem ID [2013]
Book: Mathematical methods for physics and engineering, Riley, Hobson, Bence, second edition,
2002
Section: Chapter 15, Higher order ordinary differential equations. 15.4 Exercises, page
523
Problem number: Problem 15.21.
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: 0.008 (sec). Leaf size: 20
dsolve(x^2*diff(y(x),x$2)-x*diff(y(x),x)+y(x)=x,y(x), singsol=all)
\[ y \relax (x ) = c_{2} x +\ln \relax (x ) c_{1} x +\frac {\ln \relax (x )^{2} x}{2} \]
✓ Solution by Mathematica
Time used: 0.008 (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*}