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CIE 9231 2025 June Paper 24 Q6

A Level / CIE / FP2

CIE 9231 2025 June Paper 24 Paper · Question 6

题目

Problem

Find the solution of the differential equation

xdydxy=2x2tan1xx\frac{\mathrm{d}y}{\mathrm{d}x} - y = 2x^2\tan^{-1}x

for which y=12πy = \frac{1}{2}\pi when x=1x = 1. Give your answer in the form y=f(x)y = f(x).

[9]
题目中文翻译

求微分方程

xdydxy=2x2tan1xx\frac{\mathrm{d}y}{\mathrm{d}x} - y = 2x^2\tan^{-1}x

的解,使得当 x=1x = 1y=12πy = \frac{1}{2}\pi。将答案写成 y=f(x)y = f(x) 的形式。

解答