Question

The degree of the differential equation ${\left(\frac{d^{2}y}{d{x}^2}\right)}^2-\left(\frac{dy}{dx}\right)=y^3$, is
(a) 1/2
(b) 2
(c) 3
(d) 4

Answer 1

(b) 2

We have,
${\left(\frac{d^{2}y}{d{x}^2}\right)}^2-\left(\frac{dy}{dx}\right)=y^3$
$$\begin{gathered} \mathrm{The}\mathrm{highest}\mathrm{order}\mathrm{derivative}\mathrm{is}\frac{d^{2}y}{d^{2}x}\mathrm{and}\mathrm{its}\mathrm{power}\mathrm{is}2. \\ \mathrm{Hence},\mathrm{the}\mathrm{degree}\mathrm{is}2. \end{gathered}$$