Internal problem ID [9313]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 6, non-linear second order
Problem number: 1735 (book 6.144).
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [NONE]
Solve \begin {gather*} \boxed {2 y^{\prime \prime } y-\left (y^{\prime }\right )^{2}+1+2 y^{2} x +a y^{3}=0} \end {gather*}
✗ Solution by Maple
dsolve(2*diff(diff(y(x),x),x)*y(x)-diff(y(x),x)^2+1+2*x*y(x)^2+a*y(x)^3=0,y(x), singsol=all)
\[ \text {No solution found} \]
✗ Solution by Mathematica
Time used: 0.0 (sec). Leaf size: 0
DSolve[1 + 2*x*y[x]^2 + a*y[x]^3 - y'[x]^2 + 2*y[x]*y''[x] == 0,y[x],x,IncludeSingularSolutions -> True]
Not solved