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(
1. The If c is non negative, then the solution grows exponentially large in magnitude. So the solutions diverge as t gets bigger. The boundary between solutions that ultimately grow negatively occurs when c is negative.
2. uggh...can't figure this one out.