The rate of change of y is proportional to y. When x=0, y=6, and when x=4, y=15. Write and solve the
differential equation that models this verbal statement. Then find the value of y when x=8.

Question

The rate of change of y is proportional to y. When x=0, y=6, and when x=4, y=15. Write and solve the 
differential equation that models this verbal statement. Then find the value of y when x=8.

anonymous · Answer

$y'$ is proportional to $y$. This means for any change in $y'$, the corresponding change in $y$ would be by a factor of a constant, $k$:
$$y'=ky$$
Solving it is simple, as it's separable. Given the points $(0,6)$ and $(4,15)$, you can find a particular equation.