Internal problem ID [9398]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 6, non-linear second order
Problem number: 1820 (book 6.229).
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {a \,x^{3} y^{\prime } y^{\prime \prime }+y^{2} b=0} \end {gather*}
✓ Solution by Maple
Time used: 0.078 (sec). Leaf size: 46
dsolve(a*x^3*diff(y(x),x)*diff(diff(y(x),x),x)+y(x)^2*b=0,y(x), singsol=all)
\begin{align*} y \relax (x ) = 0 \\ y \relax (x ) = {\mathrm e}^{\int _{}^{\ln \relax (x )}\RootOf \left (-\left (\int _{}^{\textit {\_Z}}\frac {\textit {\_a} a}{\textit {\_a}^{3} a -\textit {\_a}^{2} a +b}d \textit {\_a} \right )-\textit {\_b} +c_{1}\right )d \textit {\_b} +c_{2}} \\ \end{align*}
✗ Solution by Mathematica
Time used: 0.0 (sec). Leaf size: 0
DSolve[b*y[x]^2 + a*x^3*y'[x]*y''[x] == 0,y[x],x,IncludeSingularSolutions -> True]
Not solved