HSC Together Year 12 Maths Extension 1: Types of Differential Equations

#### Maths Extension 1

• Proof
• Vectors
• Further Trigonometric Functions
• Further Calculus
• Further Statistical Analysis
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# Types of Differential Equations

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.

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