Statement $1$: The degrees of the differential equations $\frac{dy}{dx} + y^2 = x$ and $\frac{d^2y}{dx^2} + y = \sin x$ are equal.
Statement $2$: The degree of a differential equation,when it is a polynomial equation in derivatives,is the highest positive integral power of the highest order derivative involved in the differential equation; otherwise,the degree is not defined.

• A
  Statement $1$ is true,Statement $2$ is true,Statement $2$ is not a correct explanation of Statement $1$.
• B
  Statement $1$ is false,Statement $2$ is true.
• C
  Statement $1$ is true,Statement $2$ is false.
• D
  Statement $1$ is true,Statement $2$ is true; Statement $2$ is a correct explanation of Statement $1$.