Find the unique solution to the initial value problem

[Colts]

Homework Statement

The unique solution to the initial value problem

is http://webwork.usi.edu/webwork2_files/tmp/equations/ed/12ad7dca5df62ed3b18f5fbf8c6e871.png
Determine the constant

and the function

Homework Equations

Not sure for the second part.

The Attempt at a Solution

I got the constant y(0)= 1 and know that is correct. I can not figure out how to get g(t). I feel like you need more information on the original problem.

 

[rude man]

Take the derivative of the solution and substitute into the diff. equation.

 

[Colts]

Thank you