Question

$\frac{d^{3}y}{d{x}^3}+{\left(\frac{d^{2}y}{d{x}^2}\right)}^3+\frac{dy}{dx}+4y=\sin x$

Answer 1

$\frac{d^{3}y}{d{x}^3}+{\left(\frac{d^{2}y}{d{x}^2}\right)}^3+\frac{dy}{dx}+4y=\sin x$

In this differential equation, the order of the highest order derivative is 3 and its power is 1. So, it is a differential equation of degree 3 and order 1.
It is a non-linear differential equation, as its differential co-efficient $\frac{d^{2}y}{d{x}^2}$ has exponent 3, which is greater than 1.