Question

$\frac{d^{3}y}{d{x}^3}+\frac{d^{2}y}{d{x}^2}+\frac{dy}{dx}+y\sin y=0$

Answer 1

$\frac{d^{3}y}{d{x}^3}+\frac{d^{2}y}{d{x}^2}+\frac{dy}{dx}+y\sin y=0$

In this differential equation, the order of the highest order derivative is 3 and its power is 1. So, the order of the differential equation is 3 and its degree is 1.

It is a non-linear differential equation, as the exponent of the dependent variable is not equal to 1 (by expanding $y.\sin y$).

Disclaimer: The answer given in the book has some error. The solution here is created according to the question given in the book.