Differential equation ( help with solving it )

[ismail amre]

Homework Statement

dy/dx = (y²-1)/(x²-1)

Homework Equations

The Attempt at a Solution

I tried to solve it by method of separation of variable and i reached
dy/(y²-1)=dx/(x²-1)
then by integrating both side i should have this answer which i got from the solution manual which is ln (y-1) - ln (y+1) = ln (x-1) - ln(x+1) .
i understand all the solution except the integration of any side of this equation dy/(y²-1)=dx/(x²-1)

 

[LCKurtz]

Homework Statement

dy/dx = (y²-1)/(x²-1)

Homework Equations

The Attempt at a Solution

I tried to solve it by method of separation of variable and i reached
dy/(y²-1)=dx/(x²-1)
then by integrating both side i should have this answer which i got from the solution manual which is ln (y-1) - ln (y+1) = ln (x-1) - ln(x+1) .
i understand all the solution except the integration of any side of this equation dy/(y²-1)=dx/(x²-1)

Use partial fractions: 1/(x²-1) = A/(x+1) + B/(x-1)

 

[ismail amre]

Use partial fractions: 1/(x²-1) = A/(x+1) + B/(x-1)

thank you very much i didn't think about that