Question

Solve differential equation dy/dx= (y^2-1)/(x^2-1)

First order differential equations
ANSWERED
asked 2021-02-20
Solve differential equation \(dy/dx= (y^2-1)/(x^2-1)\)

Answers (1)

2021-02-21

\(dy/(y^2-1)= dx/(x^2-1)\)
\(\int dy/y^2-1= \int dx/(x^2-1)\)
\(\int dy/((y-1)(y+1))= \int dx/((x-1)(x+1))\)
\(1/2 \int dy/(y-1)-1/2 \int dy/(y+1)= 1/2 \int dx/(x-1)-1/2 \int dx/(x+1)\)
\(1/2 \ln(y-1)-1/2 \ln(y+1)= 1/2 \ln(x-1)-1/2 \ln(x+1)+C\)
\(1/2 \ln((y-1)/(y+1))= 1/2 \ln ((x-1)/(x+1))+C\)
\(\ln ((y-1)/(y+1))= \ln ((x-1)/(x+1))+C\)

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