Answer
The equation of the curve is:
$y = 5~e^{2x}$
Work Step by Step
The slope of the curve is twice the y-coordinate:
$\frac{dy}{dx} = 2y$
The solution to this equation is:
$y = y(0)e^{2x}$
The curve passes through the point $(0,5)$:
$y = y(0)e^{2x}$
$y(0)e^{(2)(0)} = 5$
$y(0) = 5$
The equation of the curve is:
$y = 5~e^{2x}$
