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Solve the differential equation (dy)/(dx...

Solve the differential equation `(dy)/(dx)=(x(2logx+1))/((siny+ycosy))`.

A

`ysiny=x^(2)logx+c`

B

`ysiny=x^(2)+c`

C

`ysiny=x^(2)+logx`

D

`ysiny=xlogx+c`

Text Solution

Verified by Experts

The correct Answer is:
A
Given, `(dy)/(dx)=(xlogx^(2)+x)/(siny+ycosy)`
`implies" "(siny+ycosy)dy`
`" "=(xlogx^(2)+x)dx`
`((d)/(dy)ysiny)dy=((d)/(dx)x^(2)logx)dx`
`implies" "ysiny=x^(2)logx+c`
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