Find the unique solution to the initial value problem

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The initial value problem requires finding a unique solution based on the provided equation. The constant has been determined as y(0) = 1, which is confirmed to be correct. However, there is uncertainty regarding how to derive the function g(t). It is suggested that additional information may be necessary to solve for g(t). The approach of taking the derivative of the solution and substituting it into the differential equation is recommended for further progress.
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Homework Statement


The unique solution to the initial value problem
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is http://webwork.usi.edu/webwork2_files/tmp/equations/ed/12ad7dca5df62ed3b18f5fbf8c6e871.png
Determine the constant
311d70fb1bd53d54f2558c65e359231.png
and the function
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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.
 
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Take the derivative of the solution and substitute into the diff. equation.
 
Thank you
 

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