Q12: Order and degree of $\frac{d}{dx}(e^y) = 0$

$y$ is a function of $x$⁠, so differentiate $e^y$ by the chain rule:

The order is the order of the highest derivative present. Only the first derivative $\frac{dy}{dx}$ appears.

The degree is the highest power of the highest order derivative, once the equation is a polynomial in the derivatives. $e^y$ is a function of $y$ only, not of a derivative, so it does not stop the degree being defined. Since $e^y \ne 0$⁠, the equation is just $\frac{dy}{dx} = 0$⁠.

Watch out: "not defined", option (D), is for terms such as $e^{dy/dx}$ or $\sin\left(\frac{dy}{dx}\right)$⁠, where a derivative sits inside the function.