Question

Find the solution of the given differential equation satisfying the indicated initial condition. y’ = 0.1y, y(0) = 100

Answer 1

$$y'=0.1y\\\frac{dy}{dx}=0.1y\\\frac1ydy=0.1\,dx\\\int\frac1ydy=\int0.1\,dx\\\log y=0.1x+C\\y=e^{0.1x+C}=ce^{0.1x}\text{ where }c=e^C$$

Answer 2

Now, we solve for \(c\):$$y(0)=100\\ce^{0.1(0)}=100\\ce^0=100\\c=100$$

Answer 3

No need for integrating factors -- it's straightforward and separable at first glance.