Q3 / 105 · NTA Abhyas (JEE Main) 2020 · Mathematics · Differential Equations

The solution of the differential equation $\frac{d y}{d x} = \frac{x - y}{x + 4 y}$ is (where $C$ is the constant of integration)

A
$x y + y^{2} = x + C$
B
$x y - y^{2} = x^{2} + C$
C
$x y + 2 y^{2} = x^{2} + C$
Correct answer
D
$2 x y + 4 y^{2} = x^{2} + C$

Solution

Given equation is

x d y + 4 y d y = x d x - y d x

or

x d y + y d x + 4 y d y = x d x

or

d (x y) + 4 y d y = x d x

Integrating, we get

x y + 2 y^{2} = \frac{x^{2}}{2} + C

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

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