I've to find the general solution and determine how the solutions behave as t-->infinity.

1. y'-2y=t^(2)e^(2t)

μy'-2μy=μt^2e^(2t)

d/dt (μ(t)y(t)) = μy'+μ'y

What we need: μ' = -2μ, which is a separable equation with μ=e^(-2t)

d/dx(e^(-2t)y)=e^(-2t)t^2e^(2t)=t^2

Integrate: e^(-2t)y=t^3/3+C

Did I do this right and how does it behave?

2. y'+y= te^(-t)+1. I couldn't figure out this one 8(