Question

The equation of the curve whose slope is $\frac{dy}{dx}=\frac{2y}{x},x>0,y>0$ and passing through the point $y\left(1\right)=1$ is given by:

• A. Quadratic function
• B. Cubic function
• C. Linear function
• D. None of these

Answer 1

Answer: (A)

Quadratic function

$\frac{dy}{dx}=\frac{2y}{x}\Rightarrow \frac{\frac{dy}{dx}}{y}=\frac{2}{x}$

Integrating both sides

$\int \frac{\frac{dy}{dx}}{y}=\int \frac{2}{x}\Rightarrow \log y=2\log x+c\Rightarrow y=x^2{e}^c\Rightarrow y=x^{2}c$