What is the solution for (dP)/(dt)=P(3-P)-9/4 ?

The solution for (dP)/(dt)=P(3-P)-9/4 is P= 1/(t+c_{1)}+(3t)/(2(t+c_{1))}+(3c_{1})/(2(t+c_{1))}

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(dP)/(dt)=P(3-P)-9/4

\frac{d P}{d t} = P (3 - P) - \frac{9}{4}

P = \frac{1}{t + c _{1}} + \frac{3 t}{2 ( t + c _{1} )} + \frac{3 c _{1}}{2 ( t + c _{1} )}

Solution steps

\frac{d P}{d t} = P (3 - P) - \frac{9}{4}

Solve separable ODE:

P = \frac{1}{t + c _{1}} + \frac{3 t}{2 ( t + c _{1} )} + \frac{3 c _{1}}{2 ( t + c _{1} )}

P = \frac{1}{t + c _{1}} + \frac{3 t}{2 ( t + c _{1} )} + \frac{3 c _{1}}{2 ( t + c _{1} )}

What is the solution for (dP)/(dt)=P(3-P)-9/4 ?
The solution for (dP)/(dt)=P(3-P)-9/4 is P= 1/(t+c_{1)}+(3t)/(2(t+c_{1))}+(3c_{1})/(2(t+c_{1))}