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in Differential Equations by (35.1k points)
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The solution of the DE x dy + ydx = 0 is

A. x + y = C

B. xy = C

C. log (x + y) = C

D. None of these

1 Answer

+1 vote
by (37.0k points)
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Best answer

Given xdy + ydx = 0

xdy = -ydx

\(- \frac{dy}{y} = \frac{dx}{x}\)

On integrating on both sides we get,

-log y = log x + c

log x + log y = c

log xy = c

xy = C

Conclusion: Therefore xy = c is the solution of xdy + ydx = 0

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