\[ -f(x) ((y(x)-1) y(x) (y(x)-x))^{3/2}+2 (1-y(x)) \left (x^2-2 x y(x)+y(x)\right ) y(x) y'(x)-2 (1-x) x (1-y(x)) (x-y(x)) y(x) y''(x)+(1-x) x \left (3 y(x)^2-2 x y(x)-2 y(x)+x\right ) y'(x)^2-(1-y(x))^2 y(x)^2=0 \] ✗ Mathematica : cpu = 18.7043 (sec), leaf count = 0 , could not solve
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])*Derivative[1][y][x] + (1 - x)*x*(x - 2*y[x] - 2*x*y[x] + 3*y[x]^2)*Derivative[1][y][x]^2 - 2*(1 - x)*x*(1 - y[x])*(x - y[x])*y[x]*Derivative[2][y][x] == 0, y[x], x]
✓ Maple : cpu = 6.389 (sec), leaf count = 733
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