The solution of the differential equation, y ,dx + (x + x^2 y)dy … - Vidyadip

MCQ

The solution of the differential equation, $y\,dx + (x + {x^2}y)dy = 0$ is

A
$\log y = cx$
✓
$ - \frac{1}{{xy}} + \log y = c$
C
$\frac{1}{{xy}} - \log y = c$
D
$\frac{1}{{xy}} + \log y = c$

✓

Answer

Correct option: B.

$ - \frac{1}{{xy}} + \log y = c$

b
(b) $ydx + xdy = - {x^2}ydy$ ==> $\frac{1}{{{{(xy)}^2}}}dxy = - \frac{{dy}}{y}$

Integrating both side we get

$ - \frac{1}{{xy}} = - \log y + c$ ==> $ - \frac{1}{{xy}} + \log y = c$.

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