Internal problem ID [9206]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 6, non-linear second order
Problem number: 1627 (6.37).
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]]
Solve \begin {gather*} \boxed {y^{\prime \prime }+2 y^{\prime } y+f \relax (x ) \left (y^{2}+y^{\prime }\right )-g \relax (x )=0} \end {gather*}
✗ Solution by Maple
dsolve(diff(diff(y(x),x),x)+2*y(x)*diff(y(x),x)+f(x)*(diff(y(x),x)+y(x)^2)-g(x)=0,y(x), singsol=all)
\[ \text {No solution found} \]
✗ Solution by Mathematica
Time used: 0.0 (sec). Leaf size: 0
DSolve[-g[x] + 2*y[x]*y'[x] + f[x]*(y[x]^2 + y'[x]) + y''[x] == 0,y[x],x,IncludeSingularSolutions -> True]
Not solved