What is the solution for (dP)/(dt)=P(7-P)-49/4 ?

The solution for (dP)/(dt)=P(7-P)-49/4 is P= 1/(t+c_{1)}+(7t)/(2(t+c_{1))}+(7c_{1})/(2(t+c_{1))}

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(dP)/(dt)=P(7-P)-49/4

\frac{d P}{d t} = P (7 - P) - \frac{49}{4}

P = \frac{1}{t + c _{1}} + \frac{7 t}{2 ( t + c _{1} )} + \frac{7 c _{1}}{2 ( t + c _{1} )}

Solution steps

\frac{d P}{d t} = P (7 - P) - \frac{49}{4}

Solve separable ODE:

P = \frac{1}{t + c _{1}} + \frac{7 t}{2 ( t + c _{1} )} + \frac{7 c _{1}}{2 ( t + c _{1} )}

P = \frac{1}{t + c _{1}} + \frac{7 t}{2 ( t + c _{1} )} + \frac{7 c _{1}}{2 ( t + c _{1} )}

y^{^{'}} + \frac{3}{x} y = 0

y (1 + x^{2}) y^{^{'}} - x (1 + y^{2}) = 0, y (0) = 1

sin (y) cos (x) d y - sin (x) cos (y) d x = 0

\frac{y ^{^{'}}}{3} = x^{2} y

y^{^{'}} + 2 y + 3 = 0

What is the solution for (dP)/(dt)=P(7-P)-49/4 ?
The solution for (dP)/(dt)=P(7-P)-49/4 is P= 1/(t+c_{1)}+(7t)/(2(t+c_{1))}+(7c_{1})/(2(t+c_{1))}