The general solution of `x(dy)/(dx)=y-x tan(y/x)` is ……. .

Options

A. `x^(2)sin(x/y)=c`
B. `xsin(x/y)=c`
C. `xsin(y/x)=c`
D. `x^(2)sin(y/x)=c`

Answer

C

Explanation

We have,x`(dy)/(dx)=y-xtan(y/x)`
`rArr(dy)/(dx)=y/x-tan(y/x)`
Put `y/x=vrArry=vx`
`rArr(dy)/(dx)=v+x(dv)/(dx)`
`thereforev+x(dv)/(dx)=v-tanv`
`rArrx(dv)/(dx)=-tanv`
`rArrcotvdv=-(dx)/x`
`rArrlog(sinvdotx)=logc`
`rArrsin(y/x)dotx=c`
`rArrxsin(y/x)=c`