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

Determine order and degree(if defined) of differential equation $\left(y^{\prime \prime \prime}\right)^{2}+\left(y^{\prime \prime}\right)^{3}+\left(y^{\prime}\right)^{4}+y^{5}=0$

Solution:

$\left(y^{\prime \prime \prime}\right)^{2}+\left(y^{\prime \prime}\right)^{3}+\left(y^{\prime}\right)+y^{5}=0$

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

The given differential equation is a polynomial equation in $y^{\prime \prime \prime}, y^{\prime \prime}$, and $y^{\prime}$.

The highest power raised to $y^{\prime \prime \prime}$ is 2 . Hence, its degree is 2 .