What is the solution for ((dx)/(dy))=k(a-x)(a-x) ?

The solution for ((dx)/(dy))=k(a-x)(a-x) is x=-1/(ky+c_{1)}+(kay)/(ky+c_{1)}+(c_{1}a)/(ky+c_{1)}

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((dx)/(dy))=k(a-x)(a-x)

(\frac{d x}{d y}) = k (a - x) (a - x)

x = - \frac{1}{k y + c _{1}} + \frac{ka y}{k y + c _{1}} + \frac{c _{1} a}{k y + c _{1}}

Solution steps

(\frac{d x}{d y}) = k (a - x) (a - x)

Solve separable ODE:

x = - \frac{1}{k y + c _{1}} + \frac{ka y}{k y + c _{1}} + \frac{c _{1} a}{k y + c _{1}}

x = - \frac{1}{k y + c _{1}} + \frac{ka y}{k y + c _{1}} + \frac{c _{1} a}{k y + c _{1}}

\frac{1}{12 x}

\frac{d}{d x} (5 x - x^{- \frac{1}{3}} - 1)

\int x^{2} sec (x^{3} - 1) d x

\frac{d}{d x} (\frac{( x - 2 )}{( x + 3 ) ^{2}})

What is the solution for ((dx)/(dy))=k(a-x)(a-x) ?
The solution for ((dx)/(dy))=k(a-x)(a-x) is x=-1/(ky+c_{1)}+(kay)/(ky+c_{1)}+(c_{1}a)/(ky+c_{1)}