Let y = f(x) be a curve passing through `(e,e^( e ))` which satisfy the differential equation ` ( 2ny + xy log_(e) x ) dx - x log_(e) x dy = 0 , x gt 0, y gt 0`A. eB. 1C. 0D. 2

Let y = f(x) be a curve passing through `(e,e^( e ))` which satisfy th

1.	Let y = f(x) be a curve passing through `(e,e^( e ))` which satisfy the differential equation ` ( 2ny + xy log_(e) x ) dx - x log_(e) x dy = 0 , x gt 0, y gt 0`A. eB. 1C. 0D. 2
Answer» Correct Answer - c `2ny + xy log _(e)x) dx = x log_(e) x dy` ` rArr (dy)/y = ((2n)/(x log _(e)x)+1) dx` ` rArr log (y) = 2n log \| log x\| + x+C` ` :. " Curve through" (e,e^(e )) ` so , C = 0 ` :. y = e^(x+log(logx)2n)` ` rArr f(x) = e^(x) (log x )^(2n) ` Now, `g(x) =underset(nrarroo)lim f(x)={{:(oo","," if",xlt(1)/(e)),(0","," if ",(1)/(e)lt xlt e),(oo","," if ",x gt e):}` `therefore" "int_(1//e)^(e)g(x)dx=0`

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Let y = f(x) be a curve passing through `(e,e^( e ))` which satisfy the differential equation ` ( 2ny + xy log_(e) x ) dx - x log_(e) x dy = 0 , x gt 0, y gt 0`A. eB. 1C. 0D. 2

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