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홈 / 라이브러리 / JEE Main Master Class: Calculus, Mechanics, Coordinate Geometry / AI 플래시카드

What is the general solution to the first-order linear differential equation $\frac{dy}{dx} + P(x)y = Q(x)$?

덱 'JEE Main Master Class: Calculus, Mechanics, Coordinate Geometry'의 플래시카드.

정답

$y \cdot e^{\int P(x)dx} = \int Q(x) \cdot e^{\int P(x)dx}\,dx + C$, where $\text{IF} = e^{\int P(x)dx}$ is the integrating factor.

해설

Multiplying by the integrating factor transforms the left side into the exact derivative $\frac{d}{dx}(y \cdot \text{IF})$.

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