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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:

$V_1(t)=V_2'(t) \,k1$

$V_2(t)=V_1'(t) \,k_2+V_3'(t) \,k_3$


for $k_1,k_2,k_3,k_4$ some constants.

every input will be really helpfull. thanks.

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Do you know how to solve $v= k \, v'$? – leonbloy Jan 21 '13 at 0:26
up vote 2 down vote accepted

By writing the functions a single column vector ${\bf v}_(t)=[v_1(t),v_2(t),v_3(t)]^T$ you can rewrite your system of three linear differential equations as a single matricial one:

$${\bf v} = {\bf A} \frac{d{\bf v}}{dt}$$

where $${\bf A}=\begin{pmatrix} 0 & k_1 &0 \\ k_2 & 0 & k_3\\ 0 & k_4 & 0 \end{pmatrix}$$

Now, if you know to solve a first order linear diferential equation with constant coefficient, the procedure and the result is basically the same. See eg. Can you go on from here?

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thanks alot! this really helps! – Cain Jan 21 '13 at 22:37

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