State whether true or false: The integrating factor of \(\dfrac{dy}{dx} - y = x\) is \(e^x\).

Q.1 (B)(iii) State whether true or false: The integrating factor of \(\dfrac{dy}{dx} - y = x\) is \(e^x\).

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

1 answer

Best answer

Answer: False

Comparing with \(\dfrac{dy}{dx} + Py = Q\): \(P = -1\). I.F. \(= e^{\int P\,dx} = e^{\int -1\,dx} = e^{-x}\), not \(e^x\).

Doubtly AI · 29 Oct 2026 AI-verified · Nov 2026 Report

Was this answer helpful?