Internal problem ID [6997]
Book: Collection of Kovacic problems
Section: section 1
Problem number: 266.
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 }+\left (x^{2}+x \right ) y^{\prime }+\left (x -9\right ) y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.006 (sec). Leaf size: 40
dsolve(x^2*diff(y(x),x$2)+(x+x^2)*diff(y(x),x)+(x-9)*y(x)=0,y(x), singsol=all)
\[ y \relax (x ) = \frac {c_{1} \left (x^{2}-8 x +20\right )}{x^{3}}+\frac {c_{2} {\mathrm e}^{-x} \left (x^{3}+9 x^{2}+36 x +60\right )}{x^{3}} \]
✓ Solution by Mathematica
Time used: 0.098 (sec). Leaf size: 40
DSolve[x^2*y''[x]+(x+x^2)*y'[x]+(x-9)*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {c_1 ((x-8) x+20)-c_2 e^{-x} (x (x (x+9)+36)+60)}{x^3} \\ \end{align*}