The dynamic response of a chemical process moving from one steady$-$state

condition to another can be represented by the following $2$nd order ordinary

differential equation.

$2$

$2+4$

$$

$$

$+3=$ e$$t

$,(0)=1,(0)=0$

$($a$)$ Briefly explain the method to be followed when solving differential

equations by using the Laplace transform technique.

$(4)$

$($b$)$ Use Laplace transform techniques to solve the differential equation.

$(18)$

$($c$)$ Sketch a graph of the expected dynamic response of the system over time.

$(3)$

Note that $(0)$ represents the derivative of $$ at time $=0.$