Internal problem ID [8773]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 2, linear second order
Problem number: 1193.
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 }+x \left (x +1\right ) y^{\prime }+\left (x -9\right ) y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.005 (sec). Leaf size: 40
dsolve(x^2*diff(diff(y(x),x),x)+x*(x+1)*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: 0.095 (sec). Leaf size: 40
DSolve[(-9 + x)*y[x] + x*(1 + x)*y'[x] + x^2*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*}