Quick questions on First-order differential equations explained: H2 Further Mathematics

5short Q&A pairs drawn directly from our worked dot-point answer. For full context and worked exam questions, read the parent dot-point page.

What is recognising a separable equation?

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An equation is separable when

\dfrac{\mathrm{d}y}{\mathrm{d}x}

equals a product (or quotient) of a function of

x

and a function of

y

. If

x

and

y

are tangled additively (for example

\dfrac{\mathrm{d}y}{\mathrm{d}x} = x + y

), separation fails and the integrating factor method is the tool.

What is not in standard form before

\mu

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The integrating factor uses the coefficient of

y

when the coefficient of

\dfrac{\mathrm{d}y}{\mathrm{d}x}

1

; divide through first.

What is q1?

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State the integrating factor for

\dfrac{\mathrm{d}y}{\mathrm{d}x} + 3y = x

. [1 mark]

What is q2?

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Separate the variables in

\dfrac{\mathrm{d}y}{\mathrm{d}x} = xy

. [1 mark]

What is q3?

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Why does the integrating factor method work after multiplying through? [2 marks]

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