Chapter 7.4, Problem 12E

To determine

To calculate : the equation of the curve

Answer to Problem 12E

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

Explanation of Solution

Given information : The question is

A curve passes through the point $\left(0,5\right)$ and has the property that the slope of the curve at every point $P$ is twice the y- coordinate of $P$

Calculation : for the equation of curve

  $\begin{array}{l}y\left(0\right)=5\\ \frac{dy}{dx}=2y\\ \frac{dy}{dx}=ky\\ y\left(x\right)=y\left(0\right)e^{kx}\\ \frac{dy}{dx}=2y\\ y=5e^{2x}\end{array}$