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Differential Equations question

2024 · 5 Apr · Shift 2 · Q50

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JEE Main
Mathematics
Differential Equations
2024 · 5 Apr · Shift 2 · Q50

Differential Equations question

2024 · 5 Apr · Shift 2 · Q50

JEE MainMathematicsDifferential EquationsMCQ+4 / −1

The differential equation of the family of circles passing through the origin and having centre at the line

y=x

is :

A
$\left(x^2-y^2+2 x y\right) \mathrm{d} x=\left(x^2-y^2+2 x y\right) \mathrm{d} y$
B
$\left(x^2+y^2-2 x y\right) \mathrm{d} x=\left(x^2+y^2+2 x y\right) \mathrm{d} y$
C
$\left(x^2+y^2+2 x y\right) \mathrm{d} x=\left(x^2+y^2-2 x y\right) \mathrm{d} y$
D
$\left(x^2-y^2+2 x y\right) \mathrm{d} x=\left(x^2-y^2-2 x y\right) \mathrm{d} y$

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