If c is any arbitrary constant, then the general solution of the … - Vidyadip

MCQ

If $c$ is any arbitrary constant, then the general solution of the differential equation $ydx - xdy = xy\,dx$ is given by

A
$y = cx\,{e^{ - x}}$
B
$x = cy{e^{ - x}}$
C
$y + {e^x} = cx$
✓
$y{e^x} = cx$

✓

Answer

Correct option: D.

$y{e^x} = cx$

d
(d) Given $ydx - xdy = xydx$

==> $\frac{{ydx - xdy}}{{xy}} = dx$ ==> $d\left[ {\ln \left( {\frac{x}{y}} \right)} \right] = dx$

Integrating both sides, we get $\ln \frac{x}{y} + \ln c = x$ ==> $y{e^x} = cx$.

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