DSolve[x*F[0, 0]*y[x]^2 + x*F[1, 1]*Derivative[2][y][x] + (x*F[0, 2] + x*F[2, 0])*y[x]*Derivative[2][y][x] + x*F[2, 2]*Derivative[2][y][x]^2 + Derivative[1][y][x]*((x*F[0, 1] + x*F[1, 0])*y[x] + (x*F[1, 2] + x*F[2, 1])*Derivative[2][y][x]) == 0,y[x],x]