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

Determine order and degree(if defined) of differential equation $\frac{d^{4} y}{d x^{4}}+\sin \left(y^{\prime \prime}\right)=0$

Solution:

$\frac{d^{4} y}{d x^{4}}+\sin \left(y^{\prime \prime \prime}\right)=0$

$\Rightarrow y^{\prime \prime \prime \prime}+\sin \left(y^{\prime \prime \prime}\right)=0$

The highest order derivative present in the differential equation is $y^{\prime \prime \prime}$. Therefore, its order is four.

The highest order derivative present in the differential equation is $y^{\prime \prime \prime}$. Therefore, its order is four.