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1st order autonomous, homogeneous differential equation have the general form:

[tex]\dot{x}(t)=ax(t)[/tex]

It can be shown that the unique solution is always:

[tex]x(t)=e^{at}x(t_{0})[/tex]

I don't get this, could anyone help me?

Thanks!

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# Unique solution of 1st order autonomous, homogeneous DE

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