What is the solution for dt=(dy)/(9y-y^2-81/4) ?

The solution for dt=(dy)/(9y-y^2-81/4) is y= 1/(t+c_{1)}+(9t)/(2(t+c_{1))}+(9c_{1})/(2(t+c_{1))}

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dt=(dy)/(9y-y^2-81/4)

d t = \frac{d y}{9 y - y ^{2} - \frac{81}{4}}

y = \frac{1}{t + c _{1}} + \frac{9 t}{2 ( t + c _{1} )} + \frac{9 c _{1}}{2 ( t + c _{1} )}

Solution steps

d t = \frac{d y}{9 y - y ^{2} - \frac{81}{4}}

Solve separable ODE:

y = \frac{1}{t + c _{1}} + \frac{9 t}{2 ( t + c _{1} )} + \frac{9 c _{1}}{2 ( t + c _{1} )}

y = \frac{1}{t + c _{1}} + \frac{9 t}{2 ( t + c _{1} )} + \frac{9 c _{1}}{2 ( t + c _{1} )}

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What is the solution for dt=(dy)/(9y-y^2-81/4) ?
The solution for dt=(dy)/(9y-y^2-81/4) is y= 1/(t+c_{1)}+(9t)/(2(t+c_{1))}+(9c_{1})/(2(t+c_{1))}