60.7.226 problem 1817 (book 6.226)

Internal problem ID [11815]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 6, non-linear second order
Problem number : 1817 (book 6.226)
Date solved : Monday, January 27, 2025 at 11:37:44 PM
CAS classification : [[_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]]

\begin{align*} y^{\prime } y^{\prime \prime }-x^{2} y y^{\prime }-x y^{2}&=0 \end{align*}

✗ 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: 0.000 (sec). Leaf size: 0

DSolve[-(x*y[x]^2) - x^2*y[x]*D[y[x],x] + D[y[x],x]*D[y[x],{x,2}] == 0,y[x],x,IncludeSingularSolutions -> True]
 

Not solved