# Calculus Course/Differential Equations/1st Order Differential Equations

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## 1st Order Differential Equations[edit]

A 1st order differential equation has the form shown below

It can be shown that roots o the differential equation above is

## Proof[edit]

The above equation can be rewritten as

Then

## Summary[edit]

First ordered differential equation of the form

has a exponential root of the form

where

or