Internal problem ID [8830]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 2, linear second order
Problem number: 1250.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {\left (-a^{2}+x^{2}\right ) y^{\prime \prime }+8 x y^{\prime }+12 y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.003 (sec). Leaf size: 52
dsolve((-a^2+x^2)*diff(diff(y(x),x),x)+8*x*diff(y(x),x)+12*y(x)=0,y(x), singsol=all)
\[ y \relax (x ) = \frac {c_{1} \left (a^{2}+3 x^{2}\right )}{\left (a -x \right )^{3} \left (x +a \right )^{3}}+\frac {c_{2} x \left (3 a^{2}+x^{2}\right )}{\left (a -x \right )^{3} \left (x +a \right )^{3}} \]
✓ Solution by Mathematica
Time used: 0.026 (sec). Leaf size: 38
DSolve[12*y[x] + 8*x*y'[x] + (-a^2 + x^2)*y''[x] == 0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {\frac {c_2 \left (a^2+3 x^2\right )}{(a-x)^3}+3 c_1}{3 (a+x)^3} \\ \end{align*}