# How to compute the following

by Karapet Hayrapetyan

(Armenia, Yerevan)

X(t)=P(t)*X(0)+integral(0,t) (P(t-tau)*B*U(tau)d(tau))

where

X(0)=(0 0);

B=(1 0);

U(t)=1, t(>=0 and <=1)

U(t)= -1, t(>=1 and <=2)

t is>= 0 and <=2

P(t) is the following matrix

P(1,1) =e^t P(1,2)= 0

P(2,1)=(-e^t+e^(3t)) P(2,2)=e^(3t)

the answer must be

X(t)=( x1(t) x2(t))

x1(t)=(e^(-2) -2e^(-1) +1)e^t

x2(t)=(e^(-2)-2e^(-1)+1)(-e^t+e^(3t))+

(1/3e^(-6)-2/3e^(-3)-e^(-2)

+2e^(-1)-2/3)e^(3t)