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I have a general question concerning DEs :0

Can one use the symmetry of the equation to somehow get the solution faster?

What does such symmetry tell us?

e.g.:

[tex]\dot x=y[/tex]

[tex]\dot y=x[/tex]

is the symmetrical system to the second order DE

[tex]\ddot x-x=0[/tex]

Now we can easily see the solutions (whether e^t or e^(-t)) actually have the same properties as functions. They are even one and the same function, rotated over the y-axis!

So, is the symmetry really providing help or this is just a coincidence?

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# Symmetries in DE

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