Internal problem ID [9257]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 6, non-linear second order
Problem number: 1679 (book 6.88).
ODE order: 2.
ODE degree: 2.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {y^{\prime \prime } x^{2}-\sqrt {a \,x^{2} \left (y^{\prime }\right )^{2}+y^{2} b}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.188 (sec). Leaf size: 64
dsolve(x^2*diff(diff(y(x),x),x)-(a*x^2*diff(y(x),x)^2+y(x)^2*b)^(1/2)=0,y(x), singsol=all)
\begin{align*} y \relax (x ) = 0 \\ y \relax (x )-{\mathrm e}^{\int _{}^{\ln \relax (x )}\RootOf \left (\int _{}^{\textit {\_Z}}-\frac {y \relax (x )}{\textit {\_a}^{2} y \relax (x )-\textit {\_a} y \relax (x )-\sqrt {y \relax (x )^{2} \left (\textit {\_a}^{2} a +b \right )}}d \textit {\_a} -\textit {\_b} +c_{1}\right )d \textit {\_b} +c_{2}} = 0 \\ \end{align*}
✗ Solution by Mathematica
Time used: 0.0 (sec). Leaf size: 0
DSolve[-Sqrt[b*y[x]^2 + a*x^2*y'[x]^2] + x^2*y''[x] == 0,y[x],x,IncludeSingularSolutions -> True]
Not solved