The differential equations, find a particular solution satisfying the given condition: `x(x^2-1)(dy)/(dx)=1; y=0` when `x" "=" "2`

Explanation

$$
\begin{aligned}
&d y=\frac{1}{x\left(x^{2}-1\right)} d x \\
&\int \mathrm{dy}=\int \frac{1}{\mathrm{x}(\mathrm{x}+1)(\mathrm{x}-1)} \mathrm{dx} \\
&=\int \frac{1}{\frac{-1 \times 1}{\mathrm{x}}}+\frac{1}{\frac{-1 \times-2}{\mathrm{x}-1}}+\frac{1}{\frac{1 \times 2}{\mathrm{x}+1}} \\
&\mathrm{y}=-\log |\mathrm{x}|+\frac{1}{2} \log |\mathrm{x}-1| \\
&\text { when } \mathrm{x}=2, \mathrm{y}=0 \Rightarrow \frac{1}{2} \log |\mathrm{x}+1|+\mathrm{C} \\
&0=-\log 2+\frac{1}{2} \log 1+\frac{1}{2} \log 3+\mathrm{C} \\
...