If the order of a differential equation $\frac{d^2 y}{d x^2}-2\left(\frac{d y}{d x}\right)^3+\sin \left(\frac{d y}{d x}\right)+y=0$ is $l$ and the degree of the differential equation $\left(1+\frac{d^2 y}{d x^2}\right)^{\frac{2}{3}}=\left[2-\left(\frac{d y}{d x}\right)^3\right]^{\frac{3}{2}}$ is $m$, then the differential equation corresponding to the family of curves $y=A x^l+B e^{m x}$, where $A$ and $B$ are arbitrary constants, is

• A
  $\left(4 x^2-2 x\right) y^{\prime \prime}+\left(16 x^2-2\right) y^{\prime}+(32 x-8) y=0$
• B
  $\left(2 x^2-x\right) y^{\prime \prime}+\left(8 x^2-2\right) y^{\prime}+(16 x-4) y=0$
• C
  $\left(2 x^2-x\right) y^{\prime \prime}-\left(8 x^2-1\right) y^{\prime}+(16 x-4) y=0$
• D
  $\left(4 x^2-2 x\right) y^{\prime \prime}+\left(8 x^2-1\right) y^{\prime}+(16 x-4) y=0$