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The solution of the differential equatio...

The solution of the differential equation `y (1 + log x) (dx)/(dy) - x log x = 0` is

A

` x log x = y +C`

B

` x log x = yC`

C

` y (1+log x)C`

D

` log x-y=C`

Text Solution

Verified by Experts

The correct Answer is:
b
Given differential equation is
` y (1+log x)(dx)/(dy) - x log x = 0`
` rArr int (1+logx)/(x log x) dx = int (dy)/y`
` rArr int 1/(x log x ) dx + int 1/x dx = int 1/y dy`
` rArr log (log x) + log x = log y + log C`
` rArr x log x = yC`
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MHTCET PREVIOUS YEAR PAPERS AND PRACTICE PAPERS-DIFFERENTIAL EQUATION-MHT CET Corner
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