Question

Solve the following differential equations :
$\frac{dy}{dx}=-\frac{y}{x}$

• A. $y=\frac{2c}{x}$
• B. $y=\frac{1}{x}$
• C. $y=\frac{c}{2x}$
• D. $y=\frac{c}{x}$

Answer 1

Answer: (D)

$y=\frac{c}{x}$

$\frac{dy}{dx}=-\frac{y}{x}$

$\Rightarrow \frac{dy}{y}=-\frac{dx}{x}$

$\Rightarrow ln|y|=-(n|x|+ln|c|)$

$\Rightarrow ln|y|=ln|\frac{c}{x}|$

$\Rightarrow y=\frac{c}{x}$