# How to solve this equation

1. Sep 18, 2007

### sammyb787

1. The problem statement, all variables and given/known data

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.

2. Relevant equations

3. 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

2. Sep 18, 2007

### 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?