Solution of the equation (x + y)dy + y ,dx = 0 is - Vidyadip

MCQ

Solution of the equation $(x + \log y)dy + y\,dx = 0$ is

A
$xy + y\log y = c$
✓
$xy + y\log y - y = c$
C
$xy + \log y - x = c$
D
None of these

✓

Answer

Correct option: B.

$xy + y\log y - y = c$

b
(b) $xdy + ydx + \log ydy = 0$ ==> $xdy + ydx = - \log ydy$

$y\frac{{dx}}{{dy}} + x = - \log y$ ==> $\frac{{dx}}{{dy}} + \frac{x}{y} = - \frac{{\log y}}{y}$

$I.F.$ =${e^{\int {\frac{1}{y}dy} }} = y$

Hence solution is $x.y = - \int {y.\frac{{\log ydy}}{y} + c} $

==> $xy = - (y\log y - y) + c$ ==> $xy + (y\log y - y) = c$.

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