Question

Determine the order and degree (if defined) of the following differential equation:-

\[\left( \frac{ds}{dt} \right)^4 + 3s\frac{d^2 s}{d t^2} = 0\]

Answer 1

\[\left( \frac{ds}{dt} \right)^4 + 3s\frac{d^2 s}{d t^2} = 0\]

The highest order derivative in the given equation is \[\frac{d^2 s}{d t^2}\] and its power is 1.

Therefore, the given differential equation is of second order and first degree.
i.e., Order = 2 and degree = 1