Question

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

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

Answer 1

Answer: (C)

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