The sum of order and degree of differential equation \(\left(\displaystyle\frac{ds}{dt}\right)^4+3s\displaystyle\frac{d^2s}{dt^2}=0\), is:
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → 3
The order is the order of the highest derivative present. Here it is \(\frac{d^2s}{dt^2}\), so the order is 2.
The equation is a polynomial in the derivatives. The degree is the power of the highest-order derivative, \(\frac{d^2s}{dt^2}\), which appears to the power 1. So the degree is 1. (The power 4 belongs to \(\frac{ds}{dt}\), a lower-order derivative.)
\(\text{order} + \text{degree} = 2 + 1 = 3\)