Hello,
I am going to remember:
y'+3y=0==>y=Ce^(-3t)
y'=C'e^(-3t)-3Ce^(-3t)
y'+3y=C'e^(-3t)-3Ce^(-3t)+3Ce^(-3t)=C'e^(-3t) = t+e^(-2t)
==>C'=(t+e^(-2t))/e^(-3t)=te^(3t)+e^t
==>C=e^t+te^(3t) /3-e^(3t)/9
==>y= (e^t+te^(3t)/3-e^(3t)/9)e^(-3t)+D
==>y=e^(-2t)+t/3-1/9+D
==>y=e^(-2t)+t/3+k
