Q.1 (vii) The integrating factor of linear differential equation xdy/dx + 2y = x² log x is _____. A. x B. 1/x C. x² D. 1/x²

Answer: C. x² Answer: (c) x² Dividing by x : dy/dx + 2/xy = xlog x , which is of the form dy/dx + Py = Q with P = 2/x . I.F. = e^(∫ 2/xdx) = e^(2log x) = e^(log x^2) = x² .

The integrating factor of linear differential equation \(x\frac{dy}{dx} + 2y = x^2 \log x\) is _____.

Q.1 (vii) The integrating factor of linear differential equation \(x\frac{dy}{dx} + 2y = x^2 \log x\) is _____.

A. \(x\)

B. \(\frac{1}{x}\)

C. \(x^2\)

D. \(\frac{1}{x^2}\)

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

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Answer: C. \(x^2\)

Answer: (c) \(x^2\)

Dividing by \(x\): \(\frac{dy}{dx} + \frac{2}{x}y = x\log x\), which is of the form \(\frac{dy}{dx} + Py = Q\) with \(P = \frac{2}{x}\).

I.F. \(= e^{\int \frac{2}{x}dx} = e^{2\log x} = e^{\log x^2} = x^2\).

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

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The integrating factor of linear differential equation \(x\frac{dy}{dx} + 2y = x^2 \log x\) is _____.

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