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

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

\frac{d y}{d t} = 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

\frac{d y}{d t} = 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} )}

\frac{d}{d a} (sin^{4} (a) - cos^{4} (a) + 2 cos^{2} (a))

\int \frac{sin ( 2 x )}{1 + cos ^{4} ( x )} d x

y = \frac{x + 1}{x}

x \to - 87 lim (F (x))

\int_{0}^{1} x^{4} e^{- x} d x

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