The integrating factor of the differential eq | vedclass

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(B) To find the integrating factor,we first write the differential equation in the standard linear form $\frac{dy}{dx} + P(x)y = Q(x)$.Dividing the gi

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$\frac{1}{x}$

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(B) To find the integrating factor,we first write the differential equation in the standard linear form $\frac{dy}{dx} + P(x)y = Q(x)$.Dividing the given equation $x \frac{dy}{dx} - y = x^2$ by $x$,we get:$\frac{dy}{dx} - \frac{1}{x}y = x$.Here,$P(x) = -\frac{1}{x}$.The integrating factor $(IF)$ is given by the formula $IF = e^{\int P(x) dx}$.$IF = e^{\int -\frac{1}{x} dx} = e^{-\ln|x|} = e^{\ln|x^{-1}|} = x^{-1} = \frac{1}{x}$.Thus,the correct option is $B$.

The integrating factor of the differential equation $x \frac{dy}{dx} - y = x^2$ is . . . . . . .

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