Internal problem ID [9376]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 6, non-linear second order
Problem number: 1798 (book 6.207).
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_Painleve, 5th]]
Solve \begin {gather*} \boxed {2 x^{2} y \left (y-1\right ) y^{\prime \prime }-x^{2} \left (-1+3 y\right ) \left (y^{\prime }\right )^{2}+2 x y \left (y-1\right ) y^{\prime }+\left (a y^{2}+b \right ) \left (y-1\right )^{3}+c x y^{2} \left (y-1\right )+d \,x^{2} y^{2} \left (y+1\right )=0} \end {gather*}
✗ Solution by Maple
dsolve(2*x^2*y(x)*(-1+y(x))*diff(diff(y(x),x),x)-x^2*(3*y(x)-1)*diff(y(x),x)^2+2*x*y(x)*(-1+y(x))*diff(y(x),x)+(a*y(x)^2+b)*(-1+y(x))^3+c*x*y(x)^2*(-1+y(x))+d*x^2*y(x)^2*(y(x)+1)=0,y(x), singsol=all)
\[ \text {No solution found} \]
✗ Solution by Mathematica
Time used: 0.0 (sec). Leaf size: 0
DSolve[c*x*(-1 + y[x])*y[x]^2 + d*x^2*y[x]^2*(1 + y[x]) + (-1 + y[x])^3*(b + a*y[x]^2) + 2*x*(-1 + y[x])*y[x]*y'[x] - x^2*(-1 + 3*y[x])*y'[x]^2 + 2*x^2*(-1 + y[x])*y[x]*y''[x] == 0,y[x],x,IncludeSingularSolutions -> True]
Not solved