Confusing differential equation

[aces9113]

Homework Statement

Determine the solution to the initial value differential equation: y'=0.0016 y (1800 − y), y(0)=66

Homework Equations

Getting x's on one side and y's on the other and integrating. Then solve for c

The Attempt at a Solution

I'm in calc 2 and this is the first time we are really being introduced to differentials so I put all the y's and dy on the same side and ended up with 0.347222ln(y)-0.347222ln(y-1800)=x+c.
The y integration I did on wolfram because I was unsure how to proceed so it migh be wrong. When I try to solve for y, I get a negative in the natural log which I can't do, although there must be an answer. Please help!

 

[Dick]

The integral of dy/y=ln(|y|). That formula works for negative values of y as well. The derivative of ln(y) is 1/y and so is the derivative of ln(-y). I guess Wolfram Alpha left that possibility out. You should probably try and do the integration yourself. It's just partial fractions.

 

[aces9113]

Thank you very much for the help. Would it be possible for anyone to check my work, I got y=(2.88*e^(x)+64.43653296)/(0.0016*e^(x)+1.0357980739) but apparently this is wrong