Internal problem ID [9413]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 6, non-linear second order
Problem number: 1835 (book 6.244).
ODE order: 2.
ODE degree: 2.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {\left (y^{2}-x^{2} \left (y^{\prime }\right )^{2}+y^{\prime \prime } y x^{2}\right )^{2}-4 x y \left (y^{\prime } x -y\right )^{3}=0} \end {gather*}
✗ Solution by Maple
dsolve((y(x)^2-x^2*diff(y(x),x)^2+x^2*y(x)*diff(diff(y(x),x),x))^2-4*x*y(x)*(x*diff(y(x),x)-y(x))^3=0,y(x), singsol=all)
\[ \text {No solution found} \]
✓ Solution by Mathematica
Time used: 55.764 (sec). Leaf size: 19
DSolve[-4*x*y[x]*(-y[x] + x*y'[x])^3 + (y[x]^2 - x^2*y'[x]^2 + x^2*y[x]*y''[x])^2 == 0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to c_1 x e^{\frac {1}{-x+c_2}} \\ \end{align*}