求微分方程

的解，已知当 $x = 0$ 时 $y = 0$。答案需写成精确形式。

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。

$y$ 的系数是 $-Q'/Q$，其中 $Q=x^2+6x+5$。乘积分因子 $1/Q$ 后，把右边拆成部分分式积分。

Let $Q=(x+1)(x+5)$. On the interval $x>-1$ containing the initial point, an integrating factor is $1/Q$, since the coefficient of $y$ is $-Q'/Q$. In full,

where $Q>0$ on this interval. Multiplying by this factor and using partial fractions gives

Integrating gives $\frac yQ=\ln\big(\frac{x+1}{x+5}\big)+C$. At $x=0$ we have $y=0$, so $C=\ln5$. Therefore