Internal problem ID [8726]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 2, linear second order
Problem number: 1146.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_Emden, _Fowler]]
Solve \begin {gather*} \boxed {y^{\prime \prime } x^{2}-6 y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 15
dsolve(x^2*diff(diff(y(x),x),x)-6*y(x)=0,y(x), singsol=all)
\[ y \relax (x ) = c_{1} x^{3}+\frac {c_{2}}{x^{2}} \]
✓ Solution by Mathematica
Time used: 0.003 (sec). Leaf size: 18
DSolve[-6*y[x] + x^2*y''[x] == 0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {c_2 x^5+c_1}{x^2} \\ \end{align*}