# NMath User's Guide

35.1 Encapsulating Differential Equations (.NET, C#, CSharp, VB, Visual Basic, F#)

Class represents a first order initial value differential equation. If is the unknown function, the first order initial value problem may be stated as where denotes the first derivative of y with respect to x, F is a continuous function with bounded partial derivatives, and is the value of the unknown function y at the point .

A FirstOrderInitialValueProblem instance is constructed from a function, F, and initial value, and . The function F is encapsulated as a Func<double, double, double>, a delegate which takes two doubles and returns a double.

For example, the following code constructs a FirstOrderInitialValueProblem where :

Code Example – C# ordinary differential equations (ODE)

```Func<double, double, double> f =
delegate( double x, double y )
{
return x * x;
};

double x0 = 0.0;
double y0 = 1.0;

FirstOrderInitialValueProblem prob =
new FirstOrderInitialValueProblem( f, x0, y0 );
```

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