DSolve[f[x]*y[x] + g[x]*y[x]^2 + y[x]^4 - 2*y[x]^2*Derivative[1][y][x] + (6*y[x]^2 - (2*y[x]*Derivative[1][f][x])/f[x])*Derivative[1][y][x] - 3*Derivative[1][y][x]^2 + 4*y[x]*Derivative[2][y][x] == 0,y[x],x]