Consider the differential equation \(\frac{{dy}}{{dt}} + ay = {e^{ - bt}}\) with the initial condition y(0) = 0. Then the Laplace transform Y(s) of the solution y(t) is
1
\(\frac{1}{{\left( {s + a} \right)\left( {s + b} \right)}}\)
2
\(\frac{1}{{b\left( {s + a} \right)}}\)
3
\(\frac{1}{{a\left( {s + b} \right)}}\)
4
\(\frac{{{e^{ - a}} - {e^{ - b}}}}{{b - a}}\)