# how to find a solution the differential equations

• Sep 5th 2012, 01:36 AM
mulyak
how to find a solution the differential equations
Hi everyone, I have a question about how to find a solution the differential equations in (fig.1) in symbolic (analitical) form, but with 100 or 1000 equations. I can do it in numerical form, but I need it in symbolic forms. Also, I have a matrix of coefficients in a .txt file.
How would I do this?
Thank everyone.Hi everyone, I have a question about how to find a solution the differential equations in (fig.1) in symbolic (analitical) form, but with 100 or 1000 equations. I can do it in numerical form, but I need it in symbolic forms. Also, I have a matrix of coefficients in a .txt file.
How would I do this?
Thank everyone.
Attachment 24704
• Sep 5th 2012, 06:30 AM
HallsofIvy
Re: how to find a solution the differential equations
It's not clear to me what you are asking, or what the number of equations has to do with it.
But, it is true that, first, most differential equation do not have "analytic" solutions and second, even for those that do, you typically need to use very different solutions methods for different equations.
• Sep 6th 2012, 04:59 AM
zzephod
Re: how to find a solution the differential equations
Quote:

Originally Posted by mulyak
Hi everyone, I have a question about how to find a solution the differential equations in (fig.1) in symbolic (analitical) form, but with 100 or 1000 equations. I can do it in numerical form, but I need it in symbolic forms. Also, I have a matrix of coefficients in a .txt file.
How would I do this?
Thank everyone.Hi everyone, I have a question about how to find a solution the differential equations in (fig.1) in symbolic (analitical) form, but with 100 or 1000 equations. I can do it in numerical form, but I need it in symbolic forms. Also, I have a matrix of coefficients in a .txt file.
How would I do this?
Thank everyone.
Attachment 24704

The last equation, the constraint, is irrelevant since $\displaystyle P_{16}$ does not appear in the earlier differential equations.

The first 15 equations constitute a linear constant coefficient first order system and can be written:

$\displaystyle \frac{d}{dt}{\bf{P}}={\bf{AP}}$

which has general solution $\displaystyle {\bf{P}}={\bf{K}\exp({\bf{At}})$

.