Internal problem ID [9406]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 6, non-linear second order
Problem number: 1828 (book 6.237).
ODE order: 2.
ODE degree: 2.
CAS Maple gives this as type [[_2nd_order, _missing_y]]
Solve \begin {gather*} \boxed {a^{2} \left (y^{\prime \prime }\right )^{2}-2 a x y^{\prime \prime }+y^{\prime }=0} \end {gather*}
✓ Solution by Maple
Time used: 0.063 (sec). Leaf size: 81
dsolve(a^2*diff(diff(y(x),x),x)^2-2*a*x*diff(diff(y(x),x),x)+diff(y(x),x)=0,y(x), singsol=all)
\begin{align*} y \relax (x ) = \int \RootOf \left (-\left (\int _{\textit {\_g}}^{\textit {\_Z}}\frac {1}{x \sqrt {x^{2}-\textit {\_f}}-x^{2}+2 \textit {\_f} a}d \textit {\_f} \right )+c_{1}\right )d x +c_{2} \\ y \relax (x ) = \int \RootOf \left (-\left (\int _{\textit {\_g}}^{\textit {\_Z}}\frac {1}{x \sqrt {x^{2}-\textit {\_f}}+x^{2}-2 \textit {\_f} a}d \textit {\_f} \right )+c_{1}\right )d x +c_{2} \\ \end{align*}
✗ Solution by Mathematica
Time used: 0.0 (sec). Leaf size: 0
DSolve[y'[x] - 2*a*x*y''[x] + a^2*y''[x]^2 == 0,y[x],x,IncludeSingularSolutions -> True]
Not solved