The P.I of x2y" + xy' - y = \(\rm \frac{1}{x+1}\), x > 0 is yp(x) = x v1(x) + \(\rm \frac{1}{x}\) v2(x) then v1 and v2 are given by
1
\(v_1(x)=\frac{x^2}2\), \(v_2(x)=-\frac12(\frac{x^2}{2}+x+\log(x+1))\)
2
\(v_1(x)=\frac12\log(x+1)\), \(v_2(x)=-\frac12(\frac{x^2}{2}-x+\log(x+1))\)
3
\(v_1(x)=-\frac12\log(x+1)\), \(v_2(x)=\frac12(\frac{x^2}{2}-x+\log(x+1))\)
4
None of these