Separable Equation with Condition?

[silicon_hobo]

[SOLVED] Separable Equation with Condition?

Homework Statement

Solve.
http://www.mcp-server.com/~lush/shillmud/int3.71.JPG

Homework Equations

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

 

[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.

 

[silicon_hobo]

Wow, that seems almost too easy. Thanks.