Section 4.3 Constant-Coefficient Systems

A={{-3,1},{1,-3}}

Eigensystem[A]

y={y1[t],y2[t]}

dy={y1'[t],y2'[t]}

eqn=dy==A.y

DSolve[eqn,y,t]

Expand[%]

Factor[%]

A={{4,1},{-1,2}}

eqn=dy==A.y

DSolve[eqn,y,t]

for A -> B (k1) ->C ((Subscript[k, 2]))

Coe={{-k1,0},{k1,-k2}}

eqn=dy==Coe.y

DSolve[eqn,y,t]

Expand[%]

DSolve[{eqn,y1[0]==A0,y2[0]==0},y,t]

for A <-> B ((Subscript[k, 1]),(Subscript[k, 1r])) ->C ((Subscript[k, 2]))

Coe={{-k1,k1r},{k1,-(k2+k1r)}}

k1=2;k2=1;k1r=1;

eqn=dy==Coe.y

DSolve[eqn,y,t]

DSolve[{eqn,y1[0]==A0,y2[0]==0},y,t]