So, I have been trying to figure this problem for a while and I am just not getting anywhere.

Solve the differential equation (using separation of variables):

y' = (t+1 / y+1)^2

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These are my steps so far...

y' = (t+1)^2 * (y+1)^-2

(y+1)^2 dy/dt= (t+1)^2

Then, I integrated both sides...

y + y^2 + (1/3)(y^3) = t + t^2 + (1/3)(t^3) + C


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For some reason I am getting stuck from here... to try to solve for y.

Can I take the square root of both sides before integrating? I was trying to follow the steps my instructor gave us in class, so I did not think that I could.

[Edited on November 3, 2007 at 6:29 PM. Reason : ]

11/3/2007 6:28:07 PM

Rather than multiplying (y+1)^2 out, then finding an antiderivative, instead find an antiderivative of (y+1)^2 directly. This will make it easier to solve for y in the following step.

11/3/2007 6:41:45 PM

Thanks! That made it a lot easier... I have a way of making things more difficult than they need to be

11/3/2007 8:13:06 PM