Singapore GCE A-Level · H2 Mathematics

Differential equations

13 practice questions, each with the answer and an explanation.

Practise Differential equations now

Random questions from this topic, one at a time. You see the answer and the explanation straight after each one.

All 13 questions

Solve $\frac{d y}{d x} = 2 y$ given that $y = 3$ when $x = 0$ .
Solve $\frac{d y}{d x} = 3 y$ given that $y = 9$ when $x = 0$ .
Solve $\frac{d y}{d x} = 6 y$ given that $y = 5$ when $x = 0$ .
Solve $\frac{d y}{d x} = 4 y$ given that $y = 2$ when $x = 0$ .
Solve $\frac{d y}{d x} = 5 y$ given that $y = 7$ when $x = 0$ .
Solve $y \frac{d y}{d x} = x$ given that $y = 1$ when $x = 0$ , with $y > 0$ .
Solve $y \frac{d y}{d x} = x$ given that $y = 2$ when $x = 0$ , with $y > 0$ .
Solve $y \frac{d y}{d x} = x$ given that $y = 3$ when $x = 0$ , with $y > 0$ .
Solve $y \frac{d y}{d x} = x$ given that $y = 4$ when $x = 0$ , with $y > 0$ .
Solve $y \frac{d y}{d x} = x$ given that $y = 5$ when $x = 0$ , with $y > 0$ .
The rate of growth of a population $P$ is proportional to $P$ , so that $\frac{d P}{d t} = k P$ . If $P = 1000$ at $t = 0$ and $P = 2000$ at $t = 1$ , find $k$ .
The rate of growth of a population $P$ is proportional to $P$ , so that $\frac{d P}{d t} = k P$ . If $P = 1000$ at $t = 0$ and $P = 3000$ at $t = 1$ , find $k$ .
The rate of growth of a population $P$ is proportional to $P$ , so that $\frac{d P}{d t} = k P$ . If $P = 1000$ at $t = 0$ and $P = 4000$ at $t = 1$ , find $k$ .

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