# Question #f913b

##### 1 Answer

A simple first ordinary differential equation:

#### Explanation:

**Introduction**

Differential equations can be classified essentially on: ordinary and partial. Furthermore, they can be classified into: linear and nonlinear.

Fundamentaly. linear differential equations do not have variables in their coefficients. The simplest example are ordinary differential equations (ODEs).

The general form for linear first order ODEs:

They all have analytical solutions.

**A simple Linear ordinary differential equations**

Applying the following strategy, we can obtain the solution for any equation of this shape.

Multiply both side by

See that it takes us to conclude:

By basic calculus, we can find:

Moreover, we can conclude that:

By calculus, we can find the solution:

**Some words about the solution**

It does not matter the initial solution, it will always converge to it; it is a nice property since as long as you give enough time, the system will always come back to the initial state.

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