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

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Answer 1 · 2016-05-04T08:21:29

$rsintheta=tantheta+rcostheta(2-rsintheta)^2$

If $(r,theta)$ is in polar form and $(x,y)$ in Cartesian form the relation between them is as follows:

$x=rcostheta$ , $y=rsintheta$ , $r^2=x^2+y^2$ and $tantheta=y/x$

Hence, $y=y/x+x(2-y)^2$ can be written as

$rsintheta=(rsintheta)/(rcostheta)+rcostheta(2-rsintheta)^2$

or $rsintheta=tantheta+rcostheta(2-rsintheta)^2$

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