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Calculating the parameter value when the first derivative is 0

Posted 2 years ago

I want to get the value of the corresponding parameter t when dil=0 or dvc=0. What method can I use?

sol1 = DSolve[{l il'[t] == vl[t], c vc'[t] == ic[t], 
    ir[t] == -ic[t] + il[t], vl[t] == 24 - vc[t], vr[t] == vc[t], 
    vr[t] == r ir[t], il[0] == 0, vc[0] == 0}, {ir[t], il[t], ic[t], 
    vr[t], vl[t], vc[t]}, t];
{il[t_], vc[t_]} = {il[t], vc[t]} /. sol1[[1]];
pars1 = {r -> 22, l -> 2 10^-1, c -> 1 10^-4};
a = Evaluate[il[t] /. pars1] // Simplify;
b = Evaluate[vc[t] /. pars1] // Simplify;
dil = D[a, t] // Simplify
dvc = D[b, t] // Simplify
POSTED BY: James James
3 Replies
Posted 2 years ago

Crossposted here.

POSTED BY: Rohit Namjoshi
Solve[dil == 0, t, Reals]
(*{{t -> (11 (Log[-2 + 5 Sqrt[5]] - Log[2 + 5 Sqrt[5]]))/(400 Sqrt[5])}}*)
% // N
(*{{t -> -0.00444786}}*)

Solve[dvc == 0, t, Reals]
(* {{t -> 0}} *)

Regards M.I.

POSTED BY: Mariusz Iwaniuk
Posted 2 years ago

Thank you so much!

POSTED BY: James James
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