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what are the fixed points of the modified Euler Scheme applied to this equation and what is their stability?

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dy / dt = y ( 1 - ky )

dy / dt = y - ky^2

dy / dt - y = - ky^2

Let v = y^( - 1 )

y = 1 / v

dy / dt = ( - 1 / v^2 ) * dv / dt

( - 1 / v^2)dv / dt - ( 1 / v ) = ( - k ) ( 1 / v)^2

(dv / dt ) + v = k

e^(t ) dv / dt + ( e^t )v = ke^t

(e^t )v = ke^t + C

v = k + Ce^(- t )

y = 1 / [ k + Ce^( - t ) ]

Can someone please help me after this. did I answer the question correctly? Is my answer incomplete?