CIE 9231 2025 June Paper 21 Q7

题目

Problem

Find the solution of the differential equation

\frac{\mathrm{d}y}{\mathrm{d}x} - \frac{x + 5}{x^2 + 10x + 61}y = 1,

given that $y = 0$ when $x = 3$ . Give your answer in an exact form.

[10]

题目中文翻译

求微分方程

\frac{\mathrm{d}y}{\mathrm{d}x} - \frac{x + 5}{x^2 + 10x + 61}y = 1,

的解，已知当 $x = 3$ 时 $y = 0$ 。答案需写成精确形式。