# Question:Is it possible to Explore the solution of a parameterized ODE solution?

## Question:Is it possible to Explore the solution of a parameterized ODE solution?

Hi,

Suppose I numerically solve an ODE systems with formal parameters.
Is it possible to use Explore to visualize the solution?
(the goal is to associate for instance sliders to these parameters and to visualize easily how they act)

Here is a notional problem with only one unset parameter "a".
What I usually do to analyse the role of the parameters corresponds to the for loop.

 > restart:
 > sys := { diff(x(t), t) = a*t, x(0)=0 }:
 > sol := dsolve(sys, numeric,parameters=[a])
 (1)
 > A := [seq(1..3, 1)]: for n from 1 to numelems(A) do   sol(parameters=[A[n]]):   pic||n := plots:-odeplot(                             sol,                             [t, x(t)],                             t=0..1,                             color=ColorTools:-Color([rand()/10^12, rand()/10^12, rand()/10^12]),                             legend=A[n]                           ): end do:
 > plots:-display(seq(pic||n, n=1..numelems(A)))
 >