## Calculus: Early Transcendentals 8th Edition

The equation of the curve is: $y = 5~e^{2x}$
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: $y = 5~e^{2x}$