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# The differential equation $y\Large \frac{dy}{dx}\normalsize+x=c$ represents:\begin{array}{1 1}(A)\;family \;of \;hyperbolas & (B)\;family \;of \;parabolas \\(C)\;family \;of \;ellipses & (D)\;family\; of \;circles\end{array}

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• If a linear differential equation is of the type $\large \frac{dy}{dx}$$=f(x) then it can be solved by seperating the variables and then integrating Given y \large\frac{dy}{dx}$$+x=c$
This can be written as $y. \large \frac{dy}{dx}$$=-x+c Now seperating the variables we get, y dy=(-x+c)dx Integrating on both sides we get, \int ydy=\int (-x+c)dx => \large\frac{y^2}{2}=\large\frac{-x^2}{2}$$+cx$
Rearranging the terms we get

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