Differential Equation

renjer · 2006-05-27 20:08:24

I don't know whether I'm wrong or not, but I get different answers from Scientific Workplace when I do this Differential Equation:

y''+3y'+2y=e^(-t)

Thanks for helping.

Last edited by renjer (2006-05-27 20:09:42)

numen · 2006-05-27 20:38:47

I get the same homogenous answer, so lets see about the rest.

Let (z is a function, z(t))

, so ,

So we get

So

Let z=Ct+D, so z'=C and z''=0; then C must be 1, which gives z=t.

Whohoo, first time using these codes

Last edited by numen (2006-05-27 20:53:53)

renjer · 2006-05-27 21:17:01

The answer seems like the one I had above. Anyway, thanks for showing me another method to solve DEs.

The next question goes: y''+y'+2y=t^2+e^-t+cos t.

Do I just find y''+y'+2y'=cos t? I've already calculated for t^2 and e^-t as was shown by numen. Then after I get all these, I just add them together with A and B. Is it right?

George,Y · 2006-05-27 22:01:14

It's amazing to see someone solving a DE with a "y''" so easily.

renjer · 2006-05-28 01:22:12

Yeah DEs are actually very easy, just that sometimes I do not know the rules.

So anyone know how to answer my original question?

Ricky · 2006-05-28 02:48:26

DEs are easy to solve, when they are given to you by a teacher and made nice. But most DEs are not only difficult, but impossible, at least with today's methods. Thats why there is a lot of work in the field of approximating DEs.

Have you learned methods of solving 2nd order DEs? I would go with Variation of Parameters for this one. Let me know if you haven't, I can show you how to do it.

numen · 2006-05-28 06:31:08

Yeah, you can add them all together, you use the superposition principle (I think that's what it's called anyways). DE's are easy if you're being methodic, you rarely encounter higher grade DE's practically, I've been told.

For cosx and sinx I prefer using complex e-functions. Like cosx = Re[e^(ix)]. Try that method, it's really good imho, also if you have cos(7x) or similiar it works great.
I can give you a full solution to it later if you want, I got math exams tomorrow

Last edited by numen (2006-05-28 06:32:14)

George,Y · 2006-05-30 03:27:00

COMPLEX FUNCTION????

renjer · 2006-05-30 12:48:30

I've just learnt another way of solving DEs from lecture notes from another university.

But numen, I've never heard of solving using complex functions.

numen · 2006-05-31 02:55:55

I'd be interested in hearing what you learnt

If you want to try solving your question with complex methods, use the fact that

If you have, for example, sin(7t), you simply put a 7 in the exponent of e^(ix).

Your question is the most simple example, cos(t), so I think you can follow it quite easily.

---

We know that

from above. Let and , so we get:

,

And so

Which means that

Thus, we must have that

since all derivatives disappear, which gives

So

Which becomes

Since

, this must mean that

I hope I didn't miss anything out.

George,Y · 2006-06-03 01:04:06

That's it!
But how can i learn complex functions and differentials? What kind of books?
I'm eager to learn it, could you recommand me a book on this kinda stuff? thanks

Last edited by George,Y (2006-06-03 21:25:40)

Math Is Fun Forum

#1 2006-05-27 20:08:24

Differential Equation

#2 2006-05-27 20:38:47

Re: Differential Equation

#3 2006-05-27 21:17:01

Re: Differential Equation

#4 2006-05-27 22:01:14

Re: Differential Equation

#5 2006-05-28 01:22:12

Re: Differential Equation

#6 2006-05-28 02:48:26

Re: Differential Equation

#7 2006-05-28 06:31:08

Re: Differential Equation

#8 2006-05-30 03:27:00

Re: Differential Equation

#9 2006-05-30 12:48:30

Re: Differential Equation

#10 2006-05-31 02:55:55

Re: Differential Equation

#11 2006-06-03 01:04:06

Re: Differential Equation

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