60.7.37 problem 1627 (6.37)

Internal problem ID [11626]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 6, non-linear second order
Problem number : 1627 (6.37)
Date solved : Monday, January 27, 2025 at 11:27:49 PM
CAS classification : [[_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]]

\begin{align*} y^{\prime \prime }+2 y^{\prime } y+f \left (x \right ) \left (y^{\prime }+y^{2}\right )-g \left (x \right )&=0 \end{align*}

✗ 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: 0.000 (sec). Leaf size: 0

DSolve[-g[x] + 2*y[x]*D[y[x],x] + f[x]*(y[x]^2 + D[y[x],x]) + D[y[x],{x,2}] == 0,y[x],x,IncludeSingularSolutions -> True]
 

Not solved