(x - y) e^ x/(x - y) = k then - Vidyadip

MCQ

$(x - y){e^{x/(x - y)}} = k$ then

A
$(y - 2x){{dy} \over {dx}} + 3x - 2y = 0$
✓
$y{{dy} \over {dx}} + x - 2y = 0$
C
$a{\rm{ }}\left( {y{{dy} \over {dx}} + x - 2y} \right) = 0$
D
None of these

✓

Answer

Correct option: B.

$y{{dy} \over {dx}} + x - 2y = 0$

b
(b) Taking $\log $, we get

$\log (x - y) + \frac{x}{{x - y}} = \log k$

==> $(x - y) - (x - y)\frac{{dy}}{{dx}} + (x - y) - x + \frac{{dy}}{{dx}} = 0$

==> $y\frac{{dy}}{{dx}} + x = 2y$.

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