Internal problem ID [9367]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 6, non-linear second order
Problem number: 1789 (book 6.198).
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _reducible, _mu_xy]]
Solve \begin {gather*} \boxed {2 y \left (y-1\right ) y^{\prime \prime }-\left (-1+3 y\right ) \left (y^{\prime }\right )^{2}+4 y y^{\prime } \left (f \relax (x ) y+g \relax (x )\right )+4 y^{2} \left (y-1\right ) \left (g \relax (x )^{2}-f \relax (x )^{2}-g^{\prime }\relax (x )-f^{\prime }\relax (x )\right )=0} \end {gather*}
✗ 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: 0.0 (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])*y'[x] + (1 - 3*y[x])*y'[x]^2 - 2*(1 - y[x])*y[x]*y''[x] == 0,y[x],x,IncludeSingularSolutions -> True]
Not solved