Internal problem ID [9381]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 6, non-linear second order
Problem number: 1803 (book 6.212).
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [NONE]
Solve \begin {gather*} \boxed {2 y^{3} y^{\prime \prime }+y^{2} \left (y^{\prime }\right )^{2}-a \,x^{2}-x b -c=0} \end {gather*}
✗ 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: 0.0 (sec). Leaf size: 0
DSolve[-c - b*x - a*x^2 + y[x]^2*y'[x]^2 + 2*y[x]^3*y''[x] == 0,y[x],x,IncludeSingularSolutions -> True]
Not solved