Chapter 7.4, Problem 11E

To determine

To find the solution of the differential equation .

Answer to Problem 11E

The solution of differential equation is $y=100e^{1.5t}$ .

Explanation of Solution

Given information:

The differential equation is $\frac{dy}{dt}=ky$ where $k$ is a constant and thecondition given is $k=1.5,y\left(0\right)=100$ .

Calculation:

The differential equation is $\frac{dy}{dt}=ky$

  $\begin{array}{l}\frac{dy}{dt}=ky\\ \frac{1}{y}dy=kdt\\ \text{integrating both side}\\ {\displaystyle \int \frac{1}{y}dy=k{\displaystyle \int dt}}\\ \ln y=1.5t+A\\ y=e^{1.5t+A}\\ y=C{e}^{1.5t}\\ \text{given condition }k=1.5,y\left(0\right)=100\\ 100=C{e}^0\\ C=100\\ y=100e^{1.5t}\end{array}$

Therefore, the solution of differential equation is $y=100e^{1.5t}$ .