Question

The degree of the differential equation ${\left\{5+{\left(\frac{dy}{dx}\right)}^2\right\}}^{5/3}=x^5\left(\frac{d^{2}y}{d{x}^2}\right)$, is
(a) 4
(b) 2
(c) 5
(d) 10

Answer 1

We have,
$$\begin{gathered} {\left[5+{\left(\frac{dy}{dx}\right)}^2\right]}^{\frac{5}{3}}=x^5\left(\frac{d^{2}y}{d^{2}x}\right) \\ \mathrm{Taking}\mathrm{Cube}\mathrm{power}\mathrm{on}\mathrm{both}\mathrm{sides},\mathrm{we}\mathrm{get} \\ {\left(5+{\left(\frac{dy}{dx}\right)}^2\right)}^5=x^{15}{\left(\frac{d^{2}y}{d^{2}x}\right)}^3 \\ \mathrm{The}\mathrm{highest}\mathrm{order}\mathrm{derivative}\mathrm{is}\frac{d^{2}y}{d^{2}x}\mathrm{and}\mathrm{its}\mathrm{power}\mathrm{is}3. \\ \mathrm{Hence},\mathrm{the}\mathrm{degree}\mathrm{is}3. \end{gathered}$$


Disclaimer: The correct option is not given in the question.