how can i define a matrix as a sunction of a variable so that when i chande the independet variable,the elements of the matrix also change?

A(t):=[a[t],b[t],c[t]] ; i want to define a function like this,so that by changing the time t,the elements of the matrix also change,what should i do?

i have a very simple question that has made trouble for me,how can i factor this easy expression with respect to x?

nn := .1689228391e12*x^2-5539558.102*a[17][t]*x+23266721.99*a[18][t]*x+9251036.956*a[15][t]*x-6275707.162*a[16][t]*x+.4614468816e11*x*a[14][t];

factor(nn);

collect(nn,x,factor);

non of these expressions does not give me the answer which i want, i just want to write this expression in this way :

nn:=x*(...);

could anyone help me?thnx. 

how can i convert these equations to the vector mode ? 

eq1[t] := .4614468816e11*a[13][t]*a[14][t]+2291210.983*a[16][t]^2-.2842690977e11*a[17][t]^2-.1782456232e12*a[18][t]^2+.1689228391e12*a[13][t]^2+6406045.412*a[14][t]^2-4317791.317*a[15][t]^2+.9846526429e12*a[1][t]+.2533881291e12*a[2][t]+.3076607771e11*a[3][t]+8105875.203*a[4][t]-5054889.363*a[5][t]-34561.30764*a[6][t]-6275707.162*a[16][t]*a[13][t]-20873274.82*a[14][t]*a[16][t]-27435155.86*a[16][t]*a[15][t]-5539558.102*a[17...

i have an ode,which its derivatives are with respect to time,i want to use the output as a function of time to use it in a loop ,what should i do ?!

A:=a*diff(x(t),t,t)+b*diff(x(t),t)+c*x(t);

B:=solve(A,diff(x(t),t,t));

at first how can i define B as a function of t here?
how can i define initial conditons for this ?
for example :
a0:=diff(x(t),t,t) at time 0 (x(0)), but i do not know how to define this?

i also can not use B in a loop of time,t

when solving using output=listprocedure i face this message :

Sys:= {seq}(eq[k], k= 1..18):

fsolve(Sys, {seq}(a[k], k= 1..18),output=listprocedure):

Error, (in fsolve) output = listprocedure is an invalid option

what should i do? how can i list my output to use in latter commands? for example i want to use the output of the problem to plot an expression that the outputs are the coefficients of that expression?