题目

Problem

The variables $x$ and $y$ satisfy the differential equation

\cos2x\frac{\mathrm{d}y}{\mathrm{d}x}=\frac{4\tan2x}{\sin^2 3y},

where $0\le x<\frac14\pi$ . It is given that $y=0$ when $x=\frac16\pi$ .

Solve the differential equation to obtain the value of $x$ when $y=\frac16\pi$ . Give your answer correct to $3$ decimal places.

(8)

题目中文翻译

变量 $x$ 和 $y$ 满足微分方程

\cos2x\frac{\mathrm{d}y}{\mathrm{d}x}=\frac{4\tan2x}{\sin^2 3y},

其中 $0\le x<\frac14\pi$ 。已知当 $x=\frac16\pi$ 时， $y=0$ 。

解此微分方程，求 $y=\frac16\pi$ 时 $x$ 的值。答案保留 $3$ 位小数。

(8)

原卷通用作答要求

Answer all questions. You should use a calculator where appropriate.

You must show all necessary working clearly; no marks will be given for unsupported answers from a calculator.

Give non-exact numerical answers correct to 3 significant figures, or 1 decimal place for angles in degrees, unless a different level of accuracy is specified in the question.

请回答所有题目。适当时应使用计算器。必须清楚展示所有必要的计算过程；仅给出计算器答案而没有过程，不予评分。除非题目另有精度要求，非精确数值答案保留 3 位有效数字，以度为单位的角度保留 1 位小数。

CIE 9709 2023 June Paper 31 Q7

题目

解答