Question

Find order and degree of the following differential equations .
(i) $\frac{dy}{dx}+y=\frac{1}{\frac{dy}{dx}}$
(ii)${}_e[\frac{dy}{dx}-\frac{d^{3}y}{d{x}^3}]=ln[\frac{d^{5}y}{d{x}^5}+1]$
(iii)${\left[\right(\frac{dy}{dx}{)}^{1/3}+y]}^2=\frac{d^{2}y}{d{x}^2}$

Answer 1

(i) $\frac{dy}{dx}+y=\frac{1}{\left(\frac{dy}{dx}\right)}$

${\left(\frac{dy}{dx}\right)}^2+y\left(\frac{dy}{dx}\right)=1$

Order = $1,$ Degree = $2$

(ii) ${}_e[\frac{dy}{dx}-\frac{d^{3}y}{d{x}^3}]=ln[\frac{d^{5}y}{d{x}^5}+1]$

Order and Degree not defined.

(iii) ${({\left(\frac{dy}{dx}\right)}^{1/3}+1)}^2=\frac{d^{2}y}{d{x}^2}$

Order = $2,$ Degree = $1$