Internal problem ID [9330]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 6, non-linear second order
Problem number: 1752 (book 6.161).
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [NONE]
Solve \begin {gather*} \boxed {4 y^{\prime \prime } y-3 \left (y^{\prime }\right )^{2}+\left (6 y^{2}-\frac {2 f^{\prime }\relax (x ) y}{f \relax (x )}\right ) y^{\prime }+y^{4}-2 y^{2} y^{\prime }+g \relax (x ) y^{2}+f \relax (x ) y=0} \end {gather*}
✗ Solution by Maple
dsolve(4*diff(diff(y(x),x),x)*y(x)-3*diff(y(x),x)^2+(6*y(x)^2-2*diff(f(x),x)/f(x)*y(x))*diff(y(x),x)+y(x)^4-2*y(x)^2*diff(y(x),x)+g(x)*y(x)^2+f(x)*y(x)=0,y(x), singsol=all)
\[ \text {No solution found} \]
✗ Solution by Mathematica
Time used: 0.0 (sec). Leaf size: 0
DSolve[f[x]*y[x] + g[x]*y[x]^2 + y[x]^4 - 2*y[x]^2*y'[x] + (6*y[x]^2 - (2*y[x]*Derivative[1][f][x])/f[x])*y'[x] - 3*y'[x]^2 + 4*y[x]*y''[x] == 0,y[x],x,IncludeSingularSolutions -> True]
Not solved