Last updated on Oct 23, 2026

Particular Solutions (AQA A-Level Mathematics): Quizzes

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Particular Solutions

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What distinguishes a general solution from a particular solution?

General solution contains $+c$

When finding a particular solution, what must you determine?

The value of the constant $c$

In separation of variables, what is the first step for $\frac{dy}{dx} = xy$ ?

Multiply both sides by $dx$

What is the result of $\int \frac{1}{y} \, dy$ ?

$\ln|y| + c$

In $y = Ae^{\frac{1}{2}x^2}$ , what does $A$ represent?

A constant (equivalent to $e^c$ )

When integrating both sides of a separated equation, where is the constant needed?

On one side only

In modeling, if rate is 'proportional' to $\sqrt{x}$ , how do you write this?

Rate $= k\sqrt{x}$

If depth is 'decreasing' at rate proportional to $\sqrt{x}$ , what is $\frac{dx}{dt}$ ?

$-k\sqrt{x}$

What does $\int \frac{f'(x)}{f(x)} \, dx$ equal?

$\ln|f(x)| + c$

In $\frac{dh}{dt} = \frac{6-h}{20}$ , what is the maximum possible value of $h$ ?

$6$

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