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.

Answer 1

\(y'\) 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.