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# What is the difference between ODE & PDE?

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Ordinary Differncial Equation and Partical Differncial Equation ? Thanks a lot!

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MathWorld can tell you more. But in a nutshell (though I don''t know the precise defintions), ODEs involve complete derivatives, while PDEs involve partial derivatives.

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ODEs are easier than PDEs.

ODEs involve single-variable derivatives, PDEs involve multi-variable derivatives.

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It is not that PDEs involve multi variable derivatives at all.. ODEs can contain multivariate functions... The difference is VERY simple... if it contains ordinary (AKA total) derivatives only... it is an ODE. If it contains partial derivates, it is a PDE. In essence, a partial derivate is one in which all other parameters are considered constant while differentiating (even though they may otherwise be dependant). The major issure this leads to, is that integration constants become general functions. This means that finding solutions to PDEs is in general more complex that for ODEs... and even worse, general (non trivial) analytic solutions are often pretty meaningless.

Thanks a lot!

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The difference between ODE''s and PDE''s is I got an A in my class on ODE''s. I got a B in my class on PDE''s.

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