1.

The solution of differential equation ` (x^(2)-1) (dy)/(dx) + 2xy = 1/(x^(2)-1)` isA. ` y(x^(2)-1)=1/2 log |(x-1)/(x+1)|+C`B. ` y (x^(2)+1)=1/2 log |(x-1)/(x+1)|+C`C. ` y (x^(2)+1)=1/3 log |(x-1)/(x+1)|+C`D. `y ( x^(2)-1)=1/3 log |(x-1)/(x+1)|+C`

Answer» Correct Answer - d
The given differential equation is
` (x^(2)-1) (dy)/(dx) +2xy = 1/(x^(2)-1)`
` rArr (dy)/(dx) +(2x)/(x^(2)-1) y = 1/(x^(2)-1)^(2)`
This is a linear differential equation is
Here, `P = (2x)/(x^(2)-1) and Q = 1/(x^(2)-1)^(2)`
` :. IF = e^(int Pdx) = e^(int (2x)/(x^(2)-1)dx) = e^(log (x^(2)-1))= (x^(2)-1))`
The general solution of the given differential equation is
`y* IF int Q xx IF dx +C`
` rArr y(x^(2)-1) = int 1/(x^(2)-1)dx +C`
`rArr y (x^(2)-1) = 1/2 log |(x-1)/(x+1)| +C`


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