What is the solution for (dy)/(dt)=y(7-y)-49/4 ?

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

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(dy)/(dt)=y(7-y)-49/4

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

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

Solution steps

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

Solve separable ODE:

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

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

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