60.7.198 problem 1789 (book 6.198)

Internal problem ID [11787]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 6, non-linear second order
Problem number : 1789 (book 6.198)
Date solved : Monday, January 27, 2025 at 11:35:47 PM
CAS classification : [[_2nd_order, _reducible, _mu_xy]]

\begin{align*} 2 y \left (y-1\right ) y^{\prime \prime }-\left (3 y-1\right ) {y^{\prime }}^{2}+4 y y^{\prime } \left (f \left (x \right ) y+g \left (x \right )\right )+4 y^{2} \left (y-1\right ) \left (g \left (x \right )^{2}-f \left (x \right )^{2}-g^{\prime }\left (x \right )-f^{\prime }\left (x \right )\right )&=0 \end{align*}

✗ Solution by Maple

dsolve(2*y(x)*(-1+y(x))*diff(diff(y(x),x),x)-(3*y(x)-1)*diff(y(x),x)^2+4*y(x)*diff(y(x),x)*(f(x)*y(x)+g(x))+4*y(x)^2*(-1+y(x))*(g(x)^2-f(x)^2-diff(g(x),x)-diff(f(x),x))=0,y(x), singsol=all)
 

\[ \text {No solution found} \]

✗ Solution by Mathematica

Time used: 0.000 (sec). Leaf size: 0

DSolve[-4*(1 - y[x])*y[x]^2*(-f[x]^2 + g[x]^2 - Derivative[1][f][x] - Derivative[1][g][x]) + 4*y[x]*(g[x] + f[x]*y[x])*D[y[x],x] + (1 - 3*y[x])*D[y[x],x]^2 - 2*(1 - y[x])*y[x]*D[y[x],{x,2}] == 0,y[x],x,IncludeSingularSolutions -> True]
 

Not solved