Internal problem ID [9395]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 6, non-linear second order
Problem number: 1817 (book 6.226).
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _exact, _nonlinear], [_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_y_y1], [_2nd_order, _reducible, _mu_poly_yn]]
Solve \begin {gather*} \boxed {y^{\prime } y^{\prime \prime }-y^{\prime } y x^{2}-y^{2} x=0} \end {gather*}
✗ Solution by Maple
dsolve(diff(y(x),x)*diff(diff(y(x),x),x)-x^2*y(x)*diff(y(x),x)-x*y(x)^2=0,y(x), singsol=all)
\[ \text {No solution found} \]
✗ Solution by Mathematica
Time used: 0.0 (sec). Leaf size: 0
DSolve[-(x*y[x]^2) - x^2*y[x]*y'[x] + y'[x]*y''[x] == 0,y[x],x,IncludeSingularSolutions -> True]
Not solved