60.7.142 problem 1733 (book 6.142)

Internal problem ID [11731]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 6, non-linear second order
Problem number : 1733 (book 6.142)
Date solved : Monday, January 27, 2025 at 11:32:04 PM
CAS classification : [NONE]

\begin{align*} 2 y^{\prime \prime } y-{y^{\prime }}^{2}-4 \left (x +2 y\right ) y^{2}&=0 \end{align*}

✗ Solution by Maple

dsolve(2*diff(diff(y(x),x),x)*y(x)-diff(y(x),x)^2-4*(x+2*y(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[-4*y[x]^2*(x + 2*y[x]) - D[y[x],x]^2 + 2*y[x]*D[y[x],{x,2}] == 0,y[x],x,IncludeSingularSolutions -> True]
 

Not solved