need help solving this.

hello group.


let's say you have the following system.

{
a'[t] == -p1 a[t] - p3 c[t],
b'[t] == p3 c[t] - p2 b[t]
}

with initial conditions {a[0]==a0, b[0]== b0, c[0]==c0}

the system is underdetermined? as there are more variables then nymber
of equations?

so if i add the a'[t] and b'[t] equations to get

{
a'[t]+ b'[t] == -p1 a[t] -p2 b[t]
}

what type of method of solution is this? is the equation above
solvable? if so, how will i go about doing this?


also....

can I divide b'[t] by a'[t]? like...


b'[t] p3 c[t] - p2 b[t]
----- == ------------------
a'[t] -p1 a[t] - p3 c[t]


and if so... how do I get rid of c[t] ?

if the notation is comfusing, then above is essentially same as...

Y' p3 Z - p2 Y
--- == -------------
X' -p1 X - p3 Z



i need to get rid of Z.

is there a method of solution for the above system?


thanks all in advance.

.

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