Question

What the is the polar form of `y = (y-x)/(x^3+y)`?

Answer 1

`r^3cos^3thetasintheta+rsin^2theta=(sintheta-costheta)`

Explanation:

When polar coordinate are `(r,theta)` and corresponding Cartesian coordinates are `(x,y)`, the relation between them is `x=rcoxtheta` and `y=rsintheta` and `r^2=x^2+y^2`.

Hence `y=(y-x)/(x^3+y)` can be written as `x^3y+y^2=y-x` or

`r^4cos^3thetasintheta+r^2sin^2theta=r(sintheta-costheta)`

or `r^3cos^3thetasintheta+rsin^2theta=(sintheta-costheta)`