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Model Paper 3 — Applied Maths STD 11 Science — Question

CBSE BoardEnglish MediumSTD 11 ScienceApplied MathsModel Paper 32 Marks
Question
If $\mathrm{y}=\mathrm{x}+\frac{1}{x}$, prove that $x^{2} \frac{d y}{d x}-\mathrm{xy}+2=0$.
✓

Answer

Let assume: $y=x+\frac{1}{x}...(1)$
Diff. (1), w.r.t. 'x', we get
$\frac{d y}{d x}=\frac{d}{d x}(x)+\frac{d}{d x}\left(\frac{1}{x}\right)$
$\frac{d y}{d x}=1+\left(\frac{-1}{x^{2}}\right)$
$ \frac{d y}{d x}=1-\frac{1}{x^2} \ldots \ldots (2)$
We have to prove
$x^{2} \frac{d y}{d x}-x y+2=0$
L.H.S. $x^{2} \frac{d y}{d x}-x y+2$
$=x^{2}\left(1-\frac{1}{x^{2}}\right)-x\left(\frac{x+1}{x}\right)+2$
Using (1) and (2)
$=x^{2}-1-x^{2}-1+2$
$=0=$ R.H.S
Hence proved.

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