> with(LinearAlgebra): > K := Matrix([[-k1-k2,0,0,0],[+k1,0,0,0],[+k2,0,-k3,+k4],[0,0,+k3,-k4]]); [-k1 - k2 0 0 0 ] [ ] [ k1 0 0 0 ] K := [ ] [ k2 0 -k3 k4 ] [ ] [ 0 0 k3 -k4] > E := Eigenvectors(K); [-k3 - k4] [ ] [ 0 ] E := [ ], [ 0 ] [ ] [-k1 - k2] [ (k1 + k2) (-k3 - k4 + k1 + k2)] [ 0 0 0 ------------------------------] [ k3 k2 ] [ ] [ k1 (-k3 - k4 + k1 + k2) ] [ 0 0 1 - ----------------------- ] [ k3 k2 ] [ ] [ k1 + k2 - k4 ] [-1 1 0 - ------------ ] [ k3 ] [ ] [ k3 ] [ 1 ---- 0 1 ] [ k4 ] > v := E[1]; [-k3 - k4] [ ] [ 0 ] v := [ ] [ 0 ] [ ] [-k1 - k2] > X := E[2]; [ (k1 + k2) (-k3 - k4 + k1 + k2)] [ 0 0 0 ------------------------------] [ k3 k2 ] [ ] [ k1 (-k3 - k4 + k1 + k2) ] [ 0 0 1 - ----------------------- ] [ k3 k2 ] X := [ ] [ k1 + k2 - k4 ] [-1 1 0 - ------------ ] [ k3 ] [ ] [ k3 ] [ 1 ---- 0 1 ] [ k4 ] > L := DiagonalMatrix([exp(v[1]*t),exp(v[2]*t),exp(v[3]*t),exp(v[4]*t)]); [exp((-k3 - k4) t) 0 0 0 ] [ ] [ 0 1 0 0 ] L := [ ] [ 0 0 1 0 ] [ ] [ 0 0 0 exp((-k1 - k2) t)] > c0 := Vector ([Ao,0,0,0]); [Ao] [ ] [0 ] c0 := [ ] [0 ] [ ] [0 ] > ct := X . L . MatrixInverse(X) . c0; ct := [exp((-k1 - k2) t) Ao] [/ k1 k1 exp((-k1 - k2) t)\ ] [|------- - --------------------| Ao] [\k1 + k2 k1 + k2 / ] [/ exp((-k3 - k4) t) k3 k2 k2 k4 [|------------------------------ + ------------------- [\(-k3 - k4 + k1 + k2) (k3 + k4) (k1 + k2) (k3 + k4) (k1 + k2 - k4) exp((-k1 - k2) t) k2\ ] - -----------------------------------| Ao] (k1 + k2) (-k3 - k4 + k1 + k2) / ] [/ exp((-k3 - k4) t) k3 k2 k3 k2 [|- ------------------------------ + ------------------- [\ (-k3 - k4 + k1 + k2) (k3 + k4) (k1 + k2) (k3 + k4) exp((-k1 - k2) t) k3 k2 \ ] + ------------------------------| Ao] (k1 + k2) (-k3 - k4 + k1 + k2)/ ] > ctA := ct[1]; ctA := exp((-k1 - k2) t) Ao > ctB := ct[2]; / k1 k1 exp((-k1 - k2) t)\ ctB := |------- - --------------------| Ao \k1 + k2 k1 + k2 / > ctC := ct[3]; / exp((-k3 - k4) t) k3 k2 k2 k4 ctC := |------------------------------ + ------------------- \(-k3 - k4 + k1 + k2) (k3 + k4) (k1 + k2) (k3 + k4) (k1 + k2 - k4) exp((-k1 - k2) t) k2\ - -----------------------------------| Ao (k1 + k2) (-k3 - k4 + k1 + k2) / > ctD := ct[4]; / exp((-k3 - k4) t) k3 k2 k3 k2 ctD := |- ------------------------------ + ------------------- \ (-k3 - k4 + k1 + k2) (k3 + k4) (k1 + k2) (k3 + k4) exp((-k1 - k2) t) k3 k2 \ + ------------------------------| Ao (k1 + k2) (-k3 - k4 + k1 + k2)/ >