Separable Equation with Condition?

1. Mar 31, 2008

silicon_hobo

[SOLVED] Separable Equation with Condition?

1. The problem statement, all variables and given/known data
Solve.
http://www.mcp-server.com/~lush/shillmud/int3.71.JPG

2. Relevant equations

3. The attempt at a solution
I'm not sure how to separate this. Also, since the directions consist of only one word, I'm not sure if y(2)=2 is some kind of hint or an additional condition to be fulfilled. I'm wondering where to go after factoring t out of the top. Thanks.
http://www.mcp-server.com/~lush/shillmud/int3.72.JPG

2. Mar 31, 2008

nicksauce

Well after factoring... you separate (hence separable equations!)

$$\frac{dy}{y+3} = \frac{t}{t^2+1}dt$$

Then integrate both sides.
y(2) = 2 is an initial condition, not a hint... After solving for y(t) you will have one arbitrary constant, which can be solved for using this condition.

3. Mar 31, 2008

silicon_hobo

Wow, that seems almost too easy. Thanks.

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