\[ -\frac {a y(x)^3 f'(x)}{a+2}+\frac {a f(x)^2 y(x)^4}{(a+2)^2}-\frac {(a-1) y'(x)^2}{a}-f(x) y(x)^2 y'(x)+y(x) y''(x)=0 \] ✗ Mathematica : cpu = 20.9908 (sec), leaf count = 0 , could not solve
DSolve[(a*f[x]^2*y[x]^4)/(2 + a)^2 - (a*y[x]^3*Derivative[1][f][x])/(2 + a) - f[x]*y[x]^2*Derivative[1][y][x] - ((-1 + a)*Derivative[1][y][x]^2)/a + y[x]*Derivative[2][y][x] == 0, y[x], x]
✗ Maple : cpu = 0. (sec), leaf count = 0 , could not solve
dsolve(diff(diff(y(x),x),x)*y(x)-(a-1)/a*diff(y(x),x)^2-f(x)*y(x)^2*diff(y(x),x)+a/(a+2)^2*f(x)^2*y(x)^4-a/(a+2)*diff(f(x),x)*y(x)^3=0,y(x))