The integrating factor of $x\dfrac{dy}{dx}-y=x^{2}$ is : (a) $\log x$ (b) $\dfrac{-1}{x}$ (c) $x$ (d) $\dfrac{1}{x}$

The integrating factor of x(dy)/(dx)-y=x² is : (a) log x (b) (-1)/(x) (c) x (d) (1)/(x)

Question 34 of 43

x\dfrac{dy}{dx}-y=x^{2}

(a)

\log x

(b)

\dfrac{-1}{x}

(c)

x

(d)

\dfrac{1}{x}

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Put the equation in the form $\dfrac{dy}{dx}+Py=Q$ with $P=-\dfrac1x$ ; then $I.F.=e^{\int P\,dx}=\dfrac1x$ , option (d).

Standard linear form. Divide $x\dfrac{dy}{dx}-y=x^2$ by $x$ :

$\frac{dy}{dx}-\frac{1}{x}\,y=x.$

So $P=-\dfrac{1}{x}$ .

Integrating factor. …