The differential equation y dy dx + x = a(a is any constant) repr… - Vidyadip

MCQ

The differential equation $y\frac{{dy}}{{dx}} + x = a$($a$ is any constant) represents

A
A set of circles having centre on the $y$-axis
✓
A set of circles centre on the $x$-axis
C
A set of ellipses
D
None of these

✓

Answer

Correct option: B.

A set of circles centre on the $x$-axis

b
(b) We have $y\frac{{dy}}{{dx}} + x = a$or$ydy + xdx = adx$

Integrating, we get $\frac{{{y^2}}}{2} + \frac{{{x^2}}}{2} = ax + c$

or ${x^2} + {y^2} - 2ax + k = 0$,

which represents a set of circles having centre on $x$-axis.

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