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

Determine order and degree(if defined) of differential equation $\left(\frac{d s}{d t}\right)^{4}+3 s \frac{d^{2} s}{d t^{2}}=0$

Solution:

$\left(\frac{d s}{d t}\right)^{4}+3 \frac{d^{2} s}{d t^{2}}=0$

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

It is a polynomial equation in $\frac{d^{2} s}{d t^{2}}$ and $\frac{d s}{d t}$. The power raised to $\frac{d^{2} s}{d t^{2}}$ is 1 .

Hence, its degree is one.

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