Internal problem ID [9318]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 6, non-linear second order
Problem number: 1740 (book 6.149).
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}+4 y^{2} y^{\prime }+1+y^{2} f \relax (x )+y^{4}=0} \end {gather*}
✗ Solution by Maple
dsolve(2*diff(diff(y(x),x),x)*y(x)-diff(y(x),x)^2+4*y(x)^2*diff(y(x),x)+1+y(x)^2*f(x)+y(x)^4=0,y(x), singsol=all)
\[ \text {No solution found} \]
✗ Solution by Mathematica
Time used: 0.0 (sec). Leaf size: 0
DSolve[1 + f[x]*y[x]^2 + y[x]^4 + 4*y[x]^2*y'[x] - y'[x]^2 + 2*y[x]*y''[x] == 0,y[x],x,IncludeSingularSolutions -> True]
Not solved