Re: DSolve question

• To: mathgroup at smc.vnet.net
• Subject: [mg88788] Re: [mg88746] DSolve question
• From: Bob Hanlon <hanlonr at cox.net>
• Date: Fri, 16 May 2008 05:34:46 -0400 (EDT)

```Duty = 6/10;
SWfreq = 10^6;
Vin = 32/10;
Vout = 18/10;
L = 47*10^-8; R = 8/1000;

T = 1/SWfreq;
Dt1 = Duty*T;
Dt2 = (1 - Duty)*T;
VL2 = -Vout; VL1 = Vin - Vout;

Clear[i1, i2, i];

i1[t_] = i[t] /. DSolve[{L * i'[t] + R i[t] - VL1 == 0, i[0] == a1},
i[t], t][[1]] // FullSimplify

(a1 - 175)/E^((800000*t)/47) + 175

i2[t_] = i[t] /.
DSolve[{L * i'[t] + R i[t] - VL2 == 0, i[0] == a2}, i[t], t][[1]] //
FullSimplify

(a2 + 225)/E^((800000*t)/47) - 225

Solve[{i1[0] == i2[T], i1[Dt1] == i2[Dt1]}, {a1,
a2}][[1]] // FullSimplify

{a1 -> -((25*(7 - 16*E^(12/1175) +
9*E^(4/235)))/(-1 + E^(4/235))),
a2 -> (25*(9 - 25*E^(4/235) +
16*E^(32/1175)))/(-1 + E^(4/235))}

% // N

{a1->14.1825,a2->18.2886}

Bob Hanlon

---- igwood <igwood at yahoo.co.jp> wrote:
> Hi everyone. I'm looking for help using the result of DSolve.
> In the code below the DSolve statements in In[3] and In[4] find i1[t] and
i2[t] respectively in terms of variable t and a constant a1, a2 respective
ly. Then, numerical values for a1 and a2 will be found by simultaneous equations equating i1[t] and i2[t] in the FindRoot statement in In[7].
> However, I haven=C3=A2=C2=80=C2=99t been able to make Mathematica relate the i1[t], i2[t] in FindRoot to the i1[t], i2[t] resulting from DSolve. I =C3=A2=C2=80=C2=99ve tried several ways and finally the way below and alway=
s get errors.
> On the other hand if I COPY and PASTE the DSolve output Out[3], Out[4] following the -> into the lhs of i1[t] = lhs, then the FindRoot gives me the a1, and similar for a2..
> If anyone can instruct me on how to get the FindRoot to recognize the i1[t], i2[t] found from DSolve I would appreciate it. I guess in other words, how do I get output of DSolve to be a usable function.
>
> In my own reply to this post I will paste the example of the code where COPY/PASTE has been used as described above to give numerical values for a1, a2.
>
>
>
> In[1]:= Duty = .6; SWfreq = 1*10^6; Vin = 3.2; Vout = 1.8; L =
>  4.7*10^-7; R = 0.008;
>
> In[2]:= Dt1 =
>  Duty (1/SWfreq); Dt2 = (1 - Duty) (1/SWfreq); VL2 = - Vout; VL1 ==

>  Vin - Vout; T = 1/SWfreq;
>
> In[3]:= it1 =
>  Simplify[DSolve[{L i1'[t] + R i1[t] - VL1 == 0, i1[0] == a1}, i1[t],
>    t]]
>
> Out[3]= {{i1[t] -> 175.+ (-175. + 1. a1) E^(-17021.3 t)}}
>
> In[4]:= it2 =
>  Simplify[DSolve[{L i2'[t] + R i2[t] - VL2 == 0, i2[0] == a2}, i2[t],
>    t]]
>
> Out[4]= {{i2[t] -> -225. + (225.+ 1. a2) E^(-17021.3 t)}}
>
> In[5]:= i1[t_] = i1[t] /. it1
>
> Out[5]= {175.+ (-175. + 1. a1) E^(-17021.3 t)}
>
> In[6]:= i2[t_] = i2[t] /. it2
>
> Out[6]= {-225. + (225.+ 1. a2) E^(-17021.3 t)}
>
> In[7]:= FindRoot[{i1[0] == i2[T],
>   i1[Dt1] == i2[Dt1]},
>  {a1, 0}, {a2, 0}]
>
> During evaluation of In[7]:= Thread::tdlen: Objects of unequal length \
> in {0,{-0.983123}}+{{1.,0}} cannot be combined. >>
>
> During evaluation of In[7]:= Thread::tdlen: Objects of unequal length \
> in {{1.,0}}+{0,{-0.983123}} cannot be combined. >>
>
> During evaluation of In[7]:= Thread::tdlen: Objects of unequal length \
> in {0,{-0.989839}}+{{0.989839,0}} cannot be combined. >>
>
> During evaluation of In[7]:= General::stop: Further output of \
> Thread::tdlen will be suppressed during this calculation. >>
>
> During evaluation of In[7]:= FindRoot::njnum: The Jacobian is not a \
> matrix of numbers at {a1,a2} = {0.,0.}. >>
>
> Out[7]= {a1 -> 0., a2 -> 0.}
>

```

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