The integrating factor of the differential eq | vedclass

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Question

(D) Given the differential equation: $\sin x \frac{dy}{dx} - y \cos x = 1$. Divide the entire equation by $\sin x$ to write it in the standard form $\

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$\operatorname{cosec} x$

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(D) Given the differential equation: $\sin x \frac{dy}{dx} - y \cos x = 1$. Divide the entire equation by $\sin x$ to write it in the standard form $\frac{dy}{dx} + Py = Q$: $\frac{dy}{dx} - y \cot x = \operatorname{cosec} x$. Here,$P = -\cot x$. The integrating factor $(IF)$ is given by the formula $IF = e^{\int P dx}$. $IF = e^{\int -\cot x dx} = e^{-\ln|\sin x|} = e^{\ln|\sin x|^{-1}} = \frac{1}{\sin x} = \operatorname{cosec} x$.

The integrating factor of the differential equation $\sin x \frac{dy}{dx} - y \cos x = 1$ is

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