(A) For a linear differential equation of the form $\frac{dy}{dx} + P(x)y = Q(x)$,the integrating factor $(IF)$ is defined as $IF = e^{\int P(x) dx}$.

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(A) For a linear differential equation of the form $\frac{dy}{dx} + P(x)y = Q(x)$,the integrating factor $(IF)$ is defined as $IF = e^{\int P(x) dx}$.Let $u = e^{\int P(x) dx}$.Then,$\frac{du}{dx} = e^{\int P(x) dx} \cdot \frac{d}{dx}(\int P(x) dx) = u \cdot P(x)$.This implies $\frac{du}{dx} - P(x)u = 0$.Since the integrating factor $u$ satisfies this equation,the correct option is $\frac{dy}{dx} - P(x)y = 0$.

Class 12 Mathematics Differential Equations Linear differential equations

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The integrating factor of the linear differential equation $\frac{dy}{dx} + P(x)y = Q(x)$ is a solution of the differential equation:

AP EAMCET 2022 All AP EAMCET

A
$\frac{dy}{dx} - P(x)y = 0$
B
$\frac{dy}{dx} + P(x)y = 0$
C
$\frac{dy}{dx} - \frac{y}{x} = P(x)$
D
$\frac{dy}{dx} + \frac{x}{y} = P(x)$

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The integrating factor of the linear differential equation $\frac{dy}{dx} + P(x)y = Q(x)$ is a solution of the differential equation:

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