Answer to Question #31442 in Algebra for madu

Question

X(t) = amount of pesticide in the plant,
Y(t) = amount of pesticide in the soil,
R(t) litre = amount of pesticide applied to the plant
t = time in years
A typical model is obtained from input output frequency domain analysis
X/R=(S+3)/((S+3)(s-2)+2)
In a pristine orchard, the initial data is X(0)= 0, Y(0)=0, because the plant and the soil initially harbor no pesticide.
Represent the given transfer function X/R in the form of partial fractions.
one senior student has found the solution for X(t)/R(t) and he states that, X/R=e^(-βt )[cosh(αt) +5/√17 sinh(αt)] were Α=√17/2,β=1/2, Initially 2 litres of pesticides were sprayed on plants.[R(0)=2 litres]
Given,R(t) = 2/t^(2 )+1 Find the amount of pesticides in the plant after six months.