3
votes
3answers
189 views

Laplace integral - Asymptotic expansion

$$\int_{0}^{\infty} \frac{t^{x}}{{\cosh (t)}}dt$$ I'm trying to use Laplace's method to find the leading asymptotic behavior for x>>1, but I'm having some trouble. Could someone help me? Thanks in ...
2
votes
1answer
203 views

$\frac{dx}{dt}=-\lambda x +\epsilon x(t-a)$ series solution via Laplace method

Consider the following equation $$\frac{dx}{dt}=-\lambda x +\epsilon x(t-a), \quad x(0)=1,\quad |\epsilon|\ll1$$ where $a$ and $\lambda$ are positive constants and $x(t-a)$ means the function $x(t)$ ...