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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

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.

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 $\displaystyle {\bf{P}}={\bf{K}\exp({\bf{At}})$

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