Write the integrating factor (I.F.) of the differential equation \(\dfrac{dy}{dx}+y=e^{-x}\).

Q.2 (iv) Write the integrating factor (I.F.) of the differential equation \(\dfrac{dy}{dx}+y=e^{-x}\).

Doubtly Asked 29 Oct 2026 Board exam · July 2024 hsc 12th Save WhatsApp Report

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Answer: I.F. \(=e^x\)

The equation is linear, \(\dfrac{dy}{dx}+Py=Q\) with \(P=1\). I.F. \(=e^{\int P\,dx}=e^{\int1\,dx}=e^x\).

Doubtly AI · 29 Oct 2026 AI-generated · not yet verified Report

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