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]