Internal problem ID [9385]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 6, non-linear second order
Problem number: 1806 (book 6.216).
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type unknown
Solve \begin {gather*} \boxed {-2 x y \left (1-x \right ) \left (1-y\right ) \left (x -y\right ) y^{\prime \prime }+x \left (1-x \right ) \left (x -2 y x -2 y+3 y^{2}\right ) \left (y^{\prime }\right )^{2}+2 y \left (1-y\right ) \left (x^{2}+y-2 y x \right ) y^{\prime }-y^{2} \left (1-y\right )^{2}-f \left (y \left (y-1\right ) \left (y-x \right )\right )^{\frac {3}{2}}=0} \end {gather*}
✗ Solution by Maple
dsolve(-2*x*y(x)*(1-x)*(1-y(x))*(x-y(x))*diff(diff(y(x),x),x)+x*(1-x)*(x-2*x*y(x)-2*y(x)+3*y(x)^2)*diff(y(x),x)^2+2*y(x)*(1-y(x))*(x^2+y(x)-2*x*y(x))*diff(y(x),x)-y(x)^2*(1-y(x))^2-f*(y(x)*(-1+y(x))*(y(x)-x))^(3/2)=0,y(x), singsol=all)
\[ \text {No solution found} \]
✗ Solution by Mathematica
Time used: 0.0 (sec). Leaf size: 0
DSolve[-((1 - y[x])^2*y[x]^2) - f[x]*((-1 + y[x])*y[x]*(-x + y[x]))^(3/2) + 2*(1 - y[x])*y[x]*(x^2 + y[x] - 2*x*y[x])*y'[x] + (1 - x)*x*(x - 2*y[x] - 2*x*y[x] + 3*y[x]^2)*y'[x]^2 - 2*(1 - x)*x*(1 - y[x])*(x - y[x])*y[x]*y''[x] == 0,y[x],x,IncludeSingularSolutions -> True]
Not solved