Question

The degree of the differential equation $x=1+\frac{dy}{dx}+\frac{1}{2!}{\left(\frac{dy}{dx}\right)}^2+\frac{1}{3!}{\left(\frac{dy}{dx}\right)}^3+......$ is?

• A. $3$
• B. $1$
• C. Not defined
• D. None of these

Answer 1

Answer: (B)

$1$

$x=1+\frac{dy}{dx}+\frac{1}{2!}{\left(\frac{dy}{dx}\right)}^2+\frac{1}{3!}{\left(\frac{dy}{dx}\right)}^3+......$

$⟹x=e^{\frac{dy}{dx}}$
$⟹\log x=\frac{dy}{dx}$
Clearly, it is a differential equation of degree $1$.