Set of differential equations modeling biological system. for 3 distinct groups im trying to calculate V_1(t), expressed by: V_1(t)=V_2^' (t)k_1, V_2(t)=V_2^' (t)k_2+V_3^' (t)k_3, V_3(t)=V_2^' (t)k_4, for k_1, k_2, k_3, k_4 some constants.

bucstar11n0h

bucstar11n0h

Answered question

2022-11-14

Set of differential equations modeling biological system
Im trying to describe a moleculatr biological system using some differntial equations, However, differntial equations is not my strong side.
I'm thinking my equation set is quite trivial but i just cant seem to manage it. for 3 distinct groups im trying to calculate V 1 ( t ), expressed by:
V 1 ( t ) = V 2 ( t ) k 1
V 2 ( t ) = V 1 ( t ) k 2 + V 3 ( t ) k 3
V 3 ( t ) = V 2 ( t ) k 4
for k 1 , k 2 , k 3 , k 4 some constants.

Answer & Explanation

gortepap6yb

gortepap6yb

Beginner2022-11-15Added 19 answers

Step 1
By writing the functions a single column vector v ( t ) = [ v 1 ( t ) , v 2 ( t ) , v 3 ( t ) ] T you can rewrite your system of three linear differential equations as a single matricial one:
v = A d v d t
where
A = ( 0 k 1 0 k 2 0 k 3 0 k 4 0 )
Step 2
Now, if you know to solve a first order linear diferential equation with constant coefficient, the procedure and the result is basically the same. Can you go on from here?

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