Question

What the is the polar form of `y = y/x+x^2(2-y)^2`?

Answer 1

Use the conversion:
`x=r cos(theta)`
`y=r sin(theta)`

Now substitute:
`r sin(theta)=(rsin(theta))/(rcos(theta))+(rcos(theta))^2(2-rsin(theta))^2`

Expand the final term:
`r sin(theta)=(sin(theta))/(cos(theta))+r^2cos^2(theta)(4-2rsin(theta)+r^2sin^2(theta))`

Multiply by `cos(theta)`:
`r sin(theta)cos(theta)=sin(theta)+r^2cos^3(theta)(4-2rsin(theta)+r^2sin^2(theta))`

At this point it is not looking like the solution can be represented 'nicely'. You could try converting everything into `sin`