The differential equation y dy - dx - x - a a is any constant representsA- A set of circles having centre on the y-axisB- A set of circles centre on the x-axisC- None of theseD- A set of ellipses

The correct option is B A set of circles centre on the x axisWe have y dy/dx+x =a or ydy +xdx=adx Integrating, we get y^2/2+x^2/2=ax +c or x^2+y^2 2ax +k =0, ...

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Standard XII

Mathematics

Variable Separable Method

The different...

Question

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

A set of circles having centre on the y-axis

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A set of circles centre on the x-axis

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A set of ellipses

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None of these

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Solution

The correct option is B A set of circles centre on the x-axis
We have $y \frac{d y}{d x} + x = a$ or ydy +xdx=adx
Integrating, we get $\frac{y^{2}}{2} + \frac{x^{2}}{2} = a x + c$
or $x^{2} + y^{2} - 2 a x + k = 0$ ,
which represents a set of circles having centre on x-axis.

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The differential equation ydydx+x=a (a is any constant) represents

The correct option is B A set of circles centre on the x-axisWe have ydydx+x=a or ydy +xdx=adx Integrating, we get y22+x22=ax+c or x2+y2−2ax+k=0, which represents a set of circles having centre on x-axis.

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

The correct option is B A set of circles centre on the x-axis
We have $y \frac{d y}{d x} + x = a$ or ydy +xdx=adx
Integrating, we get $\frac{y^{2}}{2} + \frac{x^{2}}{2} = a x + c$
or $x^{2} + y^{2} - 2 a x + k = 0$ ,
which represents a set of circles having centre on x-axis.