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

Class **FirstOrderInitialValueProblem**
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 );