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

Explanation

`x(x^(2)-1)(dy)/(dx)=1`
`=dy=(1)/(x(x-1)(x+1))dx`
`implies intdy=int{-(1)/(x)+(1)/(2(x+1))+(1)/(2(x-1))}dx+c`
`implies y=-logx+(1)/(2)log(x+1)+(1)/(2)log(x-1)+c`………..`(1)`
Now, at `x=2`, `y=0`
`:. 0=-log2+(1)/(2)log3+0+c`
`implies c=(1)/(2)log(4)/(3)`
`:.` From equation `(1)`,
`y=-logx+(1)/(2)log(x+1)+(1)/(2)log(x-1)+(1)/(2)log(4)/(3)`
which is the required particular solution.