Question

The degree of the differential equation
$y(x)=1+\frac{dy}{dx}+\frac{1}{1.2}{\left(\frac{dy}{dx}\right)}^2+\frac{1}{\mathrm{1.2.3}}{\left(\frac{dy}{dx}\right)}^3+.........$ is

• A. 2
• B. 3
• C. 1
• D. none of these

Answer 1

Answer: (C)

Given that
$y(x)=1+\frac{dy}{dx}=\frac{1}{1.2}{\left(\frac{dy}{dx}\right)}^2+\frac{1}{\mathrm{1.2.3}}{\left(\frac{dy}{dx}\right)}^3+\dots \dots$
or $y(x)=1+\frac{1}{1!}\left(\frac{dy}{dx}\right)+\frac{1}{2!}{\left(\frac{dy}{dx}\right)}^2+\frac{1}{3!}{\left(\frac{dy}{dx}\right)}^3+\dots \dots$
$y(x)=e^{dy/dx}$
Taking log on both sides, we get
$\log y(x)=\frac{dy}{dx}$
$\therefore$ The degree of this equation is $1$ .