Question

\[s^2 \frac{d^2 t}{d s^2} + st\frac{dt}{ds} = s\]

Answer 1

\[s^2 \frac{d^2 t}{d s^2} + st\frac{dt}{ds} = s\]

\[ \Rightarrow s\frac{d^2 t}{d s^2} + t\frac{dt}{ds} = 1\]

In this differential equation, the order of the highest order derivative is 2 and its power is 1. So, it is a differential equation of order 2 and degree 1.

It is a non-linear differential equation, as it contains the product of the dependent variable \[\left( t \right)\]  and its differential co-efficient \[\left( \frac{dt}{ds} \right)\].