ODE No. 1757

$$(a+2)f(x)y(x{)}^2{y}^{\prime }(x)+ay(x)y^{″}(x)+ay(x{)}^3{y}^{\prime }(x)-(a-1)y^{\prime }(x{)}^2+f(x{)}^{2}y(x{)}^4=0$$ ✗ Mathematica : cpu = 9.13743 (sec), leaf count = 0

DSolve[f[x]^2*y[x]^4 + (2 + a)*f[x]*y[x]^2*Derivative[1][y][x] + a*y[x]^3*Derivative[1][y][x] - (-1 + a)*Derivative[1][y][x]^2 + a*y[x]*Derivative[2][y][x] == 0,y[x],x]
 

, could not solve

DSolve[f[x]^2*y[x]^4 + (2 + a)*f[x]*y[x]^2*Derivative[1][y][x] + a*y[x]^3*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

dsolve(a*y(x)*diff(diff(y(x),x),x)-(a-1)*diff(y(x),x)^2+(a+2)*f(x)*y(x)^2*diff(y(x),x)+f(x)^2*y(x)^4+a*diff(f(x),x)*y(x)^3=0,y(x))
 

, could not solve

dsolve(a*y(x)*diff(diff(y(x),x),x)-(a-1)*diff(y(x),x)^2+(a+2)*f(x)*y(x)^2*diff(y(x),x)+f(x)^2*y(x)^4+a*diff(f(x),x)*y(x)^3=0,y(x))