The differential equation is not in a form where and can be isolated directly

MATHEMATICS · Single correct · CBSE · Mathematics · Differential Equations · Differential Equations

Problem

The differential equation

\displaystyle \frac{dy}{dx}=1+\frac{y}{x}

is not in a form where

x

and

y

can be isolated directly. Which substitution is most likely to lead to an equation in which

x

and a single new variable can be isolated on opposite sides? (a)

v=y-x

(b)

v=\dfrac{y}{x}

(c)

v=xy

(d)

v=y+x^{2}