Question
Find the integral of
(y2-1) dx-2dy = 0
Answer :
Word Count : 261
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We are given the differential equation: [ (y^2 - 1) , dx - 2 , dy = 0 ] Rewriting in the standard form: [ \frac{dy}{dx} = \frac{y^2 - 1}{2} ] This is a separable differential equation. Separate variables: [ \frac{2 , dy}{y^2 - 1} = dx ] Factor the denominator: [ y^2 - 1 = (y - 1)(y + 1) ] Use partial fraction decomposition: [ \frac{2}{y^2 - 1} = \frac{A}{y - 1} + \frac{B}{y + 1} ] Multiply through by (y^2 - 1 = (y - 1)(y + 1)): [ 2 =
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