I have a math problem i've been struggling with and staring at it for an hour hasn't helped me. If anyone can help me with it I would be very grateful.

Right now my class is working on exponential growth and decay. I know that i have to find the integral of both sides and solve for Y but I don't know how to do so exactly.

Here's the problem:
if dy/dx=3Y(10-Y)
integrate to solve for Y

2. Originally Posted by Kalinator
I have a math problem i've been struggling with and staring at it for an hour hasn't helped me. If anyone can help me with it I would be very grateful.

Right now my class is working on exponential growth and decay. I know that i have to find the integral of both sides and solve for Y but I don't know how to do so exactly.

Here's the problem:
if dy/dx=3Y(10-Y)
integrate to solve for Y
$\displaystyle \frac {dy}{dx} = 3y(10 - y)$

$\displaystyle \Rightarrow \frac {dy}{y(10 - y)} = 3~dx$ ......multiplied both sides by $\displaystyle \frac {dx}{y(10 - y)}$

using partial fractions on $\displaystyle \frac 1{y(10 - y)}$, we obtain:

$\displaystyle \frac 1{10} \left( \frac 1y + \frac 1{10 - y} \right)~dy = 3~dx$

now integrate both sides and continue (don't forget your arbitrary constant)