Question

The degree of the differential equation $x=1+\left(\begin{array}{c}\frac{dy}{dx}\end{array}\right)+\frac{1}{2!}{\left(\begin{array}{c}\frac{dy}{dx}\end{array}\right)}^2+\frac{1}{3!}{\left(\begin{array}{c}\frac{dy}{dx}\end{array}\right)}^3+\dots$

• A. $3$
• B. $2$
• C. $1$
• D. not defined

Answer 1

Answer: (C)

$1$

It is in the form of $e^x$ expansion

$\Rightarrow x=e^{\frac{dy}{dx}}$

$\Rightarrow lnx=\frac{dy}{dx}$

Therefore order of differential equation is 1