Answer to Question #178010 in Math for Ratna

Question #178010

Find the integral of 

(y2-1) dx-2dy = 0


1
Expert's answer
2021-04-15T07:52:25-0400

"(y^{2}\u22121)dx\u22122dy=0"


"y^{2}\u22121\u22122y\u2032=0"


"y^{2}\u22121=2y'"


"\\frac{2}{y^{2}-1}dy=dx"


"\\intop\\frac{2}{y^{2}-1}dy=\\intop dx"


"\\frac{1}{2}.2 in(\\frac{y-1}{y+1})=x+ C"


"\\frac{y-1}{y+1}=e^{x+C}"


"\\frac{y-1}{y+1}=Ae^{x}"


"y-1=A(y+1)e^{x}"


"y(1-Ae^{x})=Ae^{x}+1"


"y=\\frac{1+Ae^{x}}{1-Ae^{x}}"



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