I Initial conditions for an ODE

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1. Dec 8, 2017

SeM

Hi, I am trying to solve an ODE, however, the initial conditions are not known. From PDE examples, which are quite different, I see that some examples have initial conditions given by functions, and not by constants, i.e::

y(0) = x^2

I may have not modeled the problem correctly yet, however, I see that the inhomogenous ODE should have a condition which is as such:

y(0) = cos(x)

MATLAB can't do it. Is it something that can't be done at all?

Thanks!

2. Dec 8, 2017

BvU

Do we have to guess what ODE ? Why don't you post it ?

3. Dec 8, 2017

SeM

y'' + iy' = 0

4. Dec 8, 2017

BvU

In other words, y(0) = 1 ?

(your ODE doesn't look inhomogeneous to me at all ?!)

5. Dec 8, 2017

SeM

Thanks, I think that explains it. I see this is a PDE not an ODE I want to solve. Cheers (y(0)=cos(theta)

6. Dec 8, 2017

BvU

Don't see no partial differential either. Is it me ?

7. Dec 8, 2017

SeM

It's not you, don't worry. It's me who is horribly wrong here.

8. Dec 8, 2017

Staff: Mentor

y appears to be a function of a single variable, so the above is an ODE. BTW, the solution I get, without considering an initial condition, is $y = -\frac i C e^{-it} + D = -\frac i C (\cos(t) - i\sin(t)) + D$.

9. Dec 8, 2017

SeM

Thanks Mark!

Cheers

10. Dec 8, 2017

Staff: Mentor

As C is an arbitrary constant anyway, this can be written shorter as $y=Ce^{-it} + D$.

11. Dec 8, 2017

Staff: Mentor

Right. I thought of this, but didn't let i be absorbed into the constant, so as to make things a bit clearer.