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