Internal problem ID [2522]
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]]
\[ \boxed {x^{2} y^{\prime \prime }-x y^{\prime }+y=x} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 18
dsolve(x^2*diff(y(x),x$2)-x*diff(y(x),x)+y(x)=x,y(x), singsol=all)
\[ y \left (x \right ) = x \left (c_{2} +\ln \left (x \right ) c_{1} +\frac {\ln \left (x \right )^{2}}{2}\right ) \]
✓ Solution by Mathematica
Time used: 0.019 (sec). Leaf size: 25
DSolve[x^2*y''[x]-x*y'[x]+y[x]==x,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {1}{2} x \left (\log ^2(x)+2 c_2 \log (x)+2 c_1\right ) \]