What is the solution for (dQ)/(dt)=14.5-(7Q)/(800-2t) ?

The solution for (dQ)/(dt)=14.5-(7Q)/(800-2t) is Q=2.9(-2t+800)+c_{1}(800-2t)^{7/2}

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(dQ)/(dt)=14.5-(7Q)/(800-2t)

\frac{d Q}{d t} = 14.5 - \frac{7 Q}{800 - 2 t}

Q = 2.9 (- 2 t + 800) + c_{1} (800 - 2 t)^{\frac{7}{2}}

Solution steps

\frac{d Q}{d t} = 14.5 - \frac{7 Q}{800 - 2 t}

Solve linear ODE:

Q = 2.9 (- 2 t + 800) + c_{1} (800 - 2 t)^{\frac{7}{2}}

Q = 2.9 (- 2 t + 800) + c_{1} (800 - 2 t)^{\frac{7}{2}}

What is the solution for (dQ)/(dt)=14.5-(7Q)/(800-2t) ?
The solution for (dQ)/(dt)=14.5-(7Q)/(800-2t) is Q=2.9(-2t+800)+c_{1}(800-2t)^{7/2}