A-level · Integration

Differential equationsExam-style questions

Solving first-order separable differential equations, using a cooling block of metal throughout. Writing a differential equation from a description of a rate; separating the variables; integrating both sides with one constant; turning a log into an explicit formula; using the conditions to find the constants; and reading the model — its long-term behaviour and its limits, including a logistic model that needs partial fractions.

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57 questions · A-level level · mark scheme and worked solution on each · no sign-up to try

DifficultyAll Level 2 Level 3 Level 4 Level 5

1
Solve $\dfrac{dy}{dx} = \dfrac{2x}{y}$ given that $y = 3$ when $x = 0$ .
Level 3 · 4 marksTry it
2
Find the general solution of $\dfrac{dy}{dx} = 3x^2 y$ .
Level 3 · 3 marksTry it
3
Solve $\dfrac{dy}{dx} = \dfrac{\cos x}{y}$ given that $y = 2$ when $x = 0$ .
Level 3 · 4 marksTry it
4
Solve $\dfrac{dy}{dx} = x y^2$ given that $y = 1$ when $x = 0$ , giving $y$ explicitly.
Level 3 · 4 marksTry it
5
A population $P$ satisfies $\dfrac{dP}{dt} = kP$ . It is $1000$ when $t = 0$ and $1500$ when $t = 2$ . Find $P$ in terms of $t$ .
Level 3 · 4 marksTry it

9 more questions on differential equations

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