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(A) Given differential equation is $x \frac{dy}{dx} - y = 3$.Rearranging the terms,we get $x \frac{dy}{dx} = y + 3$.Separating the variables,we have $

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Straight lines

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(A) Given differential equation is $x \frac{dy}{dx} - y = 3$.Rearranging the terms,we get $x \frac{dy}{dx} = y + 3$.Separating the variables,we have $\frac{dy}{y + 3} = \frac{dx}{x}$.Integrating both sides,we get $\int \frac{dy}{y + 3} = \int \frac{dx}{x}$.This results in $\ln|y + 3| = \ln|x| + \ln|c|$,where $c$ is the constant of integration.Taking the exponential of both sides,we get $y + 3 = cx$,or $y = cx - 3$.This is the equation of a family of straight lines passing through the point $(0, -3)$.

The solution of the differential equation $x \frac{dy}{dx} - y = 3$ represents a family of

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