Question

Equation of the curve passing through (1,3) having slope $\frac{y}{x}$ at any point is

• A. $y=3x$
• B. $y=3x^2$
• C. $x^2=3y$
• D. $x=3y$

Answer 1

The correct option is A $y=3x$

$\frac{dy}{dx}=\frac{y}{x}$
$\Rightarrow \frac{dy}{y}=\frac{dx}{x}$
$\Rightarrow logy=logx+logc$
$\Rightarrow y=cx$
$\Rightarrow (x_0,y_0)=(1,3)$
$\Rightarrow 3=c$
$\Rightarrow y=3x$