Internal problem ID [8729]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 2, linear second order
Problem number: 1149.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {y^{\prime \prime } x^{2}+\left (a x +b \right ) y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 47
dsolve(x^2*diff(diff(y(x),x),x)+(a*x+b)*y(x)=0,y(x), singsol=all)
\[ y \relax (x ) = c_{1} \sqrt {x}\, \BesselJ \left (\sqrt {1-4 b}, 2 \sqrt {a}\, \sqrt {x}\right )+c_{2} \sqrt {x}\, \BesselY \left (\sqrt {1-4 b}, 2 \sqrt {a}\, \sqrt {x}\right ) \]
✓ Solution by Mathematica
Time used: 0.034 (sec). Leaf size: 95
DSolve[(b + a*x)*y[x] + x^2*y''[x] == 0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \sqrt {a} \sqrt {x} \left (c_1 \text {Gamma}\left (1-\sqrt {1-4 b}\right ) J_{-\sqrt {1-4 b}}\left (2 \sqrt {a} \sqrt {x}\right )+c_2 \text {Gamma}\left (\sqrt {1-4 b}+1\right ) J_{\sqrt {1-4 b}}\left (2 \sqrt {a} \sqrt {x}\right )\right ) \\ \end{align*}