This is part of the HSC Mathematics Extension 1 course under the topic: Applications of Calculus, in particular, differential equations.

In this post, we will learn to ketch the graph of a particular solution given a direction field and initial conditions:

- Form a direction field (slope field) from simple first-order differential equations
- Recognise the shape of a direction field from several alternatives given the form of a differential equation, and vice versa
- Sketch several possible solution curves on a given direction field

### Direction fields (slope field)

Form a direction field (slope field) from simple first-order differential equations.

### How to write a differential equation from a slope field

Recognise the shape of a direction field from several alternatives given the form of a differential equation.

### Sketching slope fields

Sketch several possible solution curves on a given direction field.