How Do You Solve the Differential Equation to Find When the Population Doubles?

[sammyb787]

Homework Statement

A certain population has a growth rate that satisfies the differential equation:

\frac{dy}{dt}=[0.5+Sin(t)]\frac{y}{5}

If y(0)=1 find the time \tau that the population has doubled.

Homework Equations

The Attempt at a Solution

This is a simple separable differential equation but when I try to solve for t when the population has doubled I get the following equation, and I can't figure out how to solve for t. I know that the equation is correct because my calculator solved it and gave the correct answer. I'm just trying to figure out where to go from here:

2Cos(t)-t=10Ln(2)-2

Thanks

Sorry about my poor use of latex

 

[Dick]

Your calculator omitted an integration constant. You'll have to have talk with it. Seriously, when you integrate something it introduces an arbitrary constant, remember?