Separable Differential Equations: dy/dx = ky

In this video, we work through the process of solving for the general solution of a simple separable differential equation:

The general solution is obtained by separating the variables so that all y's appear on the left hand side, while the x's appear on the right hand side of the equation. Thus...

Then integrating both sides...

We get:

We can then solve for y by raising both sides to the power of e to get

then finally...

As you see, this equation represents exponential growth. We apply this general solution to an ecological problem where excess phosphates cause an algae bloom in a lake and calculate the time it takes for the surface of the lake to be covered in algae!

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