Solve the First Order Linear D.E. with the initial value

[Painguy]

Homework Statement

dy/dt=y(9-y)

y(0)=2

Homework Equations

The Attempt at a Solution

dy/(y(9-y)) = dt
∫dy/(y(9-y)) = ∫dt

partial fraction decomposition
1=A/y + B/(9-y)
1=9A-Ay +By
1/9=A
0=1/9 +B
B=-1/9

1/9∫1/y -1/9∫1/(9-y)=t+C
1/9ln|y| -1/9(ln|9-y|)
1/9(ln|y/(9-y)|)=t+C
y/(9-y) =Ke^(9t)
2/7=K

y/(9-y) =(2e^(9t))/7

I'm stuck right here. It's a little embarrassing, but I forgot how to find the solution here.

 

[mliuzzolino]

You're close. Start by multiplying both sides by (9-y), distribute, add a certain term to both sides, factor out a y, etc.