Question

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

Answer 1

$(\frac{ds}{dt})^4+3s\frac{d^2s}{dt^2}=0$
The highest order derivative present in the given differential equation is $\frac{d^2s}{dt^2}$
Therefore, its order is two.
It is polynomial equation in $\frac{d^2s}{dt^2}$ and $\frac{ds}{dt}.$
The power raised to $\frac{d^2s}{dt^2}$ is 1.

Hence, its degree is one.