Sine Integral Function Si(x)

The sine integral function

Si(x)

arises sometimes while solving first order linear ODEs. The graph of Si(x) is shown below:

Graph of Si(x)

For instance, the general solution to x2dy/dx + xy = sin x is:

(Si(x) + C)/x

The slope field and a solution curve satsifying y(1) = 2 are shown below.

dy/dx = y^2(2-y)

The curve is given by the equation:

(Si(x) + 2 - Si(1))/x

Images generated by sage.