`(dy)/(dx)-(y)/(x)+cosec((y)/(x))=0 , y = 0` यदि x = 1

Explanation

`(dy)/(dx)=(y)/(x)-(1)/(sin.(y)/(x))`
`implies v+x(dv)/(dx)=v-(1)/(sin v)`
माना `y = v x implies (dy)/(dx)=v+x(dv)/(dx)`
`implies x(dv)/(dx)=-(1)/(sinv)`
`implies -sinv dv = (dx)/(x)`
`implies -intsin v dv=int(dx)/(x)+c`
`implies cos v= log x+c`
`implies cos v=logx+c`
`implies cos.(y)/(x)=logx+c`
दिया है x = 1 पर y = 0
`therefore cos 0 = log 1 + c implies c = 1`
अतः `cos.(y)/(x)=logx+1`