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## Homework Statement

Here is the question: solve y'[t]+0.2y[t]=Sin[t] with y[0]=15.3

How do I come up with a formula for y[t]?

Thanks in advance!

## Homework Equations

y[t]= starter+e^-rt

## The Attempt at a Solution

I attempted to solve the equation as is. After doing some algebra, y[t]=15.3e^-0.2 and when put back into the original equation ( y'[t]+0.2y[t]=Sin[t]), and taking y'[t], I get 0 on the LHS of the equation which doesn't equal sin[t]. I know that isn't right. What am I doing wrong?