Q56 / 150 · MHT CET 2019 (Shift 2) · Mathematics

The solution of the differential equation $y d x - x d y = x y d x$ is ….

A
$x^{2} = e^{x} y^{2}$
Correct answer
B
$x = y e^{x}$
C
$x y = e^{x}$
D
$x^{2} y^{2} = l o g x$

Solution

We have differential equation

y d x - x d y = x y d x

\Rightarrow \frac{y d x - x d y}{x y} = d x

\Rightarrow d (l o g \frac{x}{y}) = d x

On integrating both sides, we get

\log (\frac{x}{y}) = x \Rightarrow \frac{x}{y} = e^{x}

\Rightarrow x = y e^{x}

Hence, the correct answer is option: 'B'.

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