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## 8.38 `slopefield`

To draw a slope field for the differential equation *dy/dx=f(x,y)* (or
*dy/dx=f(x)*), use:

picture slopefield(real f(real,real), pair a, pair b, int nx=nmesh, int ny=nx, real tickfactor=0.5, pen p=currentpen, arrowbar arrow=None);

Here, the points `a`

and `b`

are the lower left and upper
right corners of the rectangle in which the slope field is to be drawn,
`nx`

and `ny`

are the respective number of ticks in the
*x* and *y* directions, `tickfactor`

is the fraction of
the minimum cell dimension to use for drawing ticks, and `p`

is
the pen to use for drawing the slope fields.
The return value is a picture that can be added to
`currentpicture`

via the `add(picture)`

command.

path curve(pair c, real f(real,real), pair a, pair b);

takes a point (`c`

) and a slope field-defining function `f`

and returns, as a path, the curve passing through that point. The points
`a`

and `b`

represent the rectangular boundaries over which
the curve is interpolated.

Both `slopefield`

and `curve`

alternatively accept a function
`real f(real)`

that depends on *x* only, as seen in this example:

import slopefield; size(200); real func(real x) {return 2x;} add(slopefield(func,(-3,-3),(3,3),20,Arrow)); draw(curve((0,0),func,(-3,-3),(3,3)),red);

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