60.7.216 problem 1806 (book 6.216)

Internal problem ID [11805]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 6, non-linear second order
Problem number : 1806 (book 6.216)
Date solved : Monday, January 27, 2025 at 11:36:46 PM
CAS classification : unknown

\begin{align*} -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 ) {y^{\prime }}^{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 )^{{3}/{2}}&=0 \end{align*}

✗ 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: 0.000 (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])*D[y[x],x] + (1 - x)*x*(x - 2*y[x] - 2*x*y[x] + 3*y[x]^2)*D[y[x],x]^2 - 2*(1 - x)*x*(1 - y[x])*(x - y[x])*y[x]*D[y[x],{x,2}] == 0,y[x],x,IncludeSingularSolutions -> True]
 

Not solved