Question

Write the degree of the differential equation $a^2\frac{d^{2}y}{d{x}^2}={\left\{1+{\left(\frac{dy}{dx}\right)}^2\right\}}^{1/4}$.

Answer 1

$$\begin{gathered} \mathrm{We}\mathrm{have}, \\ {a}^2\frac{d^{2}y}{d{x}^2}={\left\{1+{\left(\frac{dy}{dx}\right)}^2\right\}}^{1/4} \\ {\left\{a^2\frac{d^{2}y}{d{x}^2}\right\}}^4=1+{\left(\frac{dy}{dx}\right)}^2 \\ \mathrm{Degree}\mathrm{of}\mathrm{the}\mathrm{differential}\mathrm{equation}\mathrm{is}\mathrm{the}\mathrm{degree}\mathrm{of}\mathrm{the}\mathrm{highest}\mathrm{order}\mathrm{derivative}. \\ \mathrm{Therefore},\mathrm{the}\mathrm{degree}\mathrm{must}\mathrm{be}4. \end{gathered}$$