Internal problem ID [8734]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 2, linear second order
Problem number: 1154.
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^{2}+x b +c \right ) y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.031 (sec). Leaf size: 57
dsolve(x^2*diff(diff(y(x),x),x)+(a*x^2+b*x+c)*y(x)=0,y(x), singsol=all)
\[ y \relax (x ) = c_{1} \WhittakerM \left (-\frac {i b}{2 \sqrt {a}}, \frac {\sqrt {1-4 c}}{2}, 2 i \sqrt {a}\, x \right )+c_{2} \WhittakerW \left (-\frac {i b}{2 \sqrt {a}}, \frac {\sqrt {1-4 c}}{2}, 2 i \sqrt {a}\, x \right ) \]
✓ Solution by Mathematica
Time used: 0.009 (sec). Leaf size: 88
DSolve[(c + b*x + a*x^2)*y[x] + x^2*y''[x] == 0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to c_1 M_{-\frac {i b}{2 \sqrt {a}},-\frac {1}{2} i \sqrt {4 c-1}}\left (2 i \sqrt {a} x\right )+c_2 W_{-\frac {i b}{2 \sqrt {a}},-\frac {1}{2} i \sqrt {4 c-1}}\left (2 i \sqrt {a} x\right ) \\ \end{align*}