I have a parameter set list and I would like to solve a system of ODEs multiple times using each parameter set in the list. Then I would like each set of solutions to be graphed on the same plot.
For example:
I have imported this list of parameter sets:
{{ "a", "b", "c", "d"}, {1, 5, 1, 3}, {2, 3, 2, 2}, {3, 3, 3, 1}}
Then I have this system
system={x'[t] == a*x[t] + b*y[t], y'[t] == c*x[t] + d*y[t], x[0] == 10, y[0] == 0};
I would like to substitute each parameter set in for a,b,c,d respectively, then solve using
sol = DSolve[system, {x[t], y[t]}, {t}]
for each parameter set (or NDSolve, ParametricNDSolve if appropriate)
Then I would like all sets of solutions to be plotted on the same graph
Plot[{x[t] /. sol, y[t] /. sol}, {t, 0, 7}, PlotRange -> Automatic].
Note, I would like to use this example to understand the process and apply it to a larger system with more parameters and a larger list of sets of parameters.