# normal_ode

normal_ode, a MATLAB code which sets up and solves an ordinary differential equation (ODE) for the normal probability density function (PDF).

The normal probability density function (PDF) can be written as

```        y(t) = 1/sqrt(2 pi) e^(-t^2/2)
```
The derivative of the normal PDF is
```        y'(t) = -t/sqrt(2 pi) e^(-t^2/2) = - t * y(t)
```

Thus, along with an initial condition, an ODE for the normal PDF can be written either as:

```        y'(t) = -t/sqrt(2 pi) e^(-t^2/2)
```
or
```        y'(t) = -t * y(t)
```
While both of these ODE's have the same solution, an ODE solver will generally have more difficulty solving the second version.

### Languages:

normal_ode is available in a MATLAB version and an Octave version and a Python version.

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### Source Code:

Last revised on 04 May 2021.