Trouble Solving y'+2y=g(t): Seeking Guidance

[newtomath]

I am having trouble with part of this question:

y'+2y= g(t) where g(t) =1 for 0<t<1 and g(t)= 0 t>1 and y(0)=0

I found y= 1/2 - (1/2 * e^-2t) for 0<t<1 but am having trouble with g(t)= 0.

I know y = Ce^-2t. y(0)=0 doesn't apply here since t>1 correct? Can you point me in the right direction?

 

[Office_Shredder]

I am having trouble with part of this question:

y'+2y= g(t) where g(t) =1 for 0<t<1 and g(t)= 0 t>1 and y(0)=0

I found y= 1/2 - (1/2 * e^-2t) for 0<t<1 but am having trouble with g(t)= 0.

I know y = Ce^-2t. y(0)=0 doesn't apply here since t>1 correct? Can you point me in the right direction?

What properties do you think the graph of y(t) should have at t=1?

 

[newtomath]

should be undefined correct?