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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.

The function

```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;}
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