Internal problem ID [10080]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 6, non-linear second order
Problem number: 1758 (book 6.167).
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [NONE]
\[ \boxed {y^{\prime \prime } y a -\left (-1+a \right ) {y^{\prime }}^{2}+\left (a +2\right ) f \left (x \right ) y^{2} y^{\prime }+f \left (x \right )^{2} y^{4}+a f^{\prime }\left (x \right ) y^{3}=0} \]
✗ Solution by Maple
dsolve(a*y(x)*diff(diff(y(x),x),x)-(a-1)*diff(y(x),x)^2+(a+2)*f(x)*y(x)^2*diff(y(x),x)+f(x)^2*y(x)^4+a*diff(f(x),x)*y(x)^3=0,y(x), singsol=all)
\[ \text {No solution found} \]
✗ Solution by Mathematica
Time used: 0.0 (sec). Leaf size: 0
DSolve[f[x]^2*y[x]^4 + (2 + a)*f[x]*y[x]^2*y'[x] + a*y[x]^3*y'[x] - (-1 + a)*y'[x]^2 + a*y[x]*y''[x] == 0,y[x],x,IncludeSingularSolutions -> True]
Not solved