The differential equation yfrac{dy}{dx} + x = | vedclass

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(B) Given differential equation is $y\frac{dy}{dx} + x = a$.Separating the variables,we get $y \, dy = (a - x) \, dx$.Integrating both sides,we get $\

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

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(B) Given differential equation is $y\frac{dy}{dx} + x = a$.Separating the variables,we get $y \, dy = (a - x) \, dx$.Integrating both sides,we get $\int y \, dy = \int (a - x) \, dx$.$\frac{y^2}{2} = ax - \frac{x^2}{2} + C$,where $C$ is the constant of integration.Multiplying by $2$,we get $y^2 = 2ax - x^2 + 2C$.Rearranging the terms,we get $x^2 - 2ax + y^2 = 2C$.Adding $a^2$ to both sides,we get $(x^2 - 2ax + a^2) + y^2 = a^2 + 2C$.$(x - a)^2 + y^2 = a^2 + 2C$.Let $k = a^2 + 2C$,then $(x - a)^2 + y^2 = k$.This is the equation of a set of circles with center at $(a, 0)$,which lies on the $x$-axis.

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

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