Question

The degree of the differential equation ${\left(\frac{d^{2}y}{d{x}^2}\right)}^3+{\left(\frac{dy}{dx}\right)}^2+\sin \left(\frac{dy}{dx}\right)+1=0$, is
(a) 3
(b) 2
(c) 1
(d) not defined

Answer 1

(d) not defined

We have,
${\left(\frac{d^{2}y}{d{x}^2}\right)}^3+{\left(\frac{dy}{dx}\right)}^2+\sin \left(\frac{dy}{dx}\right)+1=0$
$$\begin{gathered} \mathrm{The}\mathrm{highest}\mathrm{order}\mathrm{derivative}\mathrm{in}\mathrm{this}\mathrm{equation}\mathrm{is}\frac{d^{2}y}{d^{2}x}. \\ \mathrm{But}\mathrm{the}\mathrm{equation}\mathrm{cannot}\mathrm{be}\mathrm{expressed}\mathrm{as}\mathrm{a}\mathrm{polynomial}\mathrm{in}\mathrm{differential}\mathrm{coefficient}. \\ \mathrm{Hence},\mathrm{the}\mathrm{degree}\mathrm{is}\mathrm{not}\mathrm{defined}. \end{gathered}$$