60.7.212 problem 1803 (book 6.212)

Internal problem ID [11801]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 6, non-linear second order
Problem number : 1803 (book 6.212)
Date solved : Monday, January 27, 2025 at 11:36:03 PM
CAS classification : [NONE]

\begin{align*} 2 y^{3} y^{\prime \prime }+y^{2} {y^{\prime }}^{2}-a \,x^{2}-b x -c&=0 \end{align*}

✗ Solution by Maple

dsolve(2*y(x)^3*diff(diff(y(x),x),x)+y(x)^2*diff(y(x),x)^2-a*x^2-b*x-c=0,y(x), singsol=all)
 

\[ \text {No solution found} \]

✗ Solution by Mathematica

Time used: 0.000 (sec). Leaf size: 0

DSolve[-c - b*x - a*x^2 + y[x]^2*D[y[x],x]^2 + 2*y[x]^3*D[y[x],{x,2}] == 0,y[x],x,IncludeSingularSolutions -> True]
 

Not solved