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Differential Equations

It is an equation whose derivative is defined by some function of it's dependent and independent variables, ie y˙=f(x,y).

An important example of a DE is y˙=ay. Which basically says that the rate of change of y is proportional to y… Sounds familiar.

dydx=ay dyy=adx ln(y)+c1=ax+c2 y=eax+(c2c1) y=Ceaxwhere C=ec2c1

We have rediscovered the canonical exponential where growth is a > 1 and decay is a < 1.

1. Associated Notes

Author: Jahan PD

Created: 2024-06-10 Mon 16:54

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