The solution of the differential equation xfr | vedclass

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(A) The given differential equation is $x\frac{dy}{dx} + y = x^2 + 3x + 2$.Dividing both sides by $x$,we get $\frac{dy}{dx} + \frac{1}{x}y = x + 3 + \

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$xy = \frac{x^3}{3} + \frac{3}{2}x^2 + 2x + c$

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(A) The given differential equation is $x\frac{dy}{dx} + y = x^2 + 3x + 2$.Dividing both sides by $x$,we get $\frac{dy}{dx} + \frac{1}{x}y = x + 3 + \frac{2}{x}$.This is a linear differential equation of the form $\frac{dy}{dx} + Py = Q$,where $P = \frac{1}{x}$ and $Q = x + 3 + \frac{2}{x}$.The integrating factor $(I.F.)$ is $e^{\int P dx} = e^{\int \frac{1}{x} dx} = e^{\ln x} = x$.The solution is given by $y(I.F.) = \int Q(I.F.) dx + c$.Substituting the values,$y(x) = \int (x + 3 + \frac{2}{x})x dx + c$.$xy = \int (x^2 + 3x + 2) dx + c$.$xy = \frac{x^3}{3} + \frac{3x^2}{2} + 2x + c$.

The solution of the differential equation $x\frac{dy}{dx} + y = x^2 + 3x + 2$ is

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