Question

Use appropriate algebra and theorem 7.2.1 to find the given inverse laplace transform. (write your answer as a function of t.) −1 s (s − 5)(s − 6)(s − 30)

Answer 1

When it comes to laplace equations, there are transformation equations to follow. Generally, when you want to transform a laplace equation, you change the equation from f(t) to F(s). If you do the reverse, it is called the reverse laplace equation.

Based on the given, the useful transformation equation is shown in the attached picture. The given equation is

$\frac{-1}{s(s-5)(s-6)(s-30)}$

Breaking it into partial fractions,

$\frac{-1}{s} * \frac{1}{s-5} * \frac{1}{s-6} * \frac{1}{s-30}$

From the given transformation equation:

-1/s ⇔ -e^0t ⇔ 1
1/(s-5) ⇔ e^-(-5t) ⇔ e^5t
1/(s-6) ⇔ e^-(-6t) ⇔ e^6t
1/(s-30) ⇔ e^-(-30t) ⇔ e^30t

Therefore, the laplace equation is equal to 1*e^5t*e^6t*e^30t which is simplified into e^41t,