Internal problem ID [8862]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 2, linear second order
Problem number: 1282.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {4 y^{\prime \prime } x^{2}+4 x^{3} y^{\prime }+\left (x^{2}+6\right ) \left (x^{2}-4\right ) y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 27
dsolve(4*x^2*diff(diff(y(x),x),x)+4*x^3*diff(y(x),x)+(x^2+6)*(x^2-4)*y(x)=0,y(x), singsol=all)
\[ y \relax (x ) = \frac {c_{1} {\mathrm e}^{-\frac {x^{2}}{4}}}{x^{2}}+c_{2} x^{3} {\mathrm e}^{-\frac {x^{2}}{4}} \]
✓ Solution by Mathematica
Time used: 0.01 (sec). Leaf size: 32
DSolve[(-4 + x^2)*(6 + x^2)*y[x] + 4*x^3*y'[x] + 4*x^2*y''[x] == 0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {e^{-\frac {x^2}{4}} \left (c_2 x^5+5 c_1\right )}{5 x^2} \\ \end{align*}