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Question

Mathematics Question on Differential equations

The solution of the differential equation xdy + ydx = 0 is:

A

xy = c

B

x2+y2=cx^2 + y^2 = c

C

xy log x = 1

D

log xy = c

Answer

xy = c

Explanation

Solution

Given, xdy + ydx = 0 Divide both sides above equation by xy, We get, dxdy+dyy=0\frac{dx}{dy} + \frac{dy}{y} = 0 Integrating it on both sides, we get log x + log y = log c ⇒\Rightarrow log xy = log c ⇒\Rightarrow xy = c.