Determine order and degree(if defined) of differential equation
Question:

Determine order and degree(if defined) of differential equation $\left(\frac{d^{2} y}{d x^{2}}\right)^{2}+\cos \left(\frac{d y}{d x}\right)=0$

Solution:

$\left(\frac{d^{2} y}{d x^{2}}\right)^{2}+\cos \left(\frac{d y}{d x}\right)=0$

The highest order derivative present in the given differential equation is $\frac{d^{2} y}{d x^{2}}$. Therefore, its order is 2 .

The given differential equation is not a polynomial equation in its derivatives. Hence, its degree is not defined.