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

1 Answer
Shwetank Mauria
Jul 3, 2016

#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)#

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