What is the solution for (dP)/(dt)= P/2-100Pe^{-2t} ?

The solution for (dP)/(dt)= P/2-100Pe^{-2t} is P=e^{1/2 (t+100e^{-2t})+c_{1}}

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(dP)/(dt)= P/2-100Pe^{-2t}

\frac{d P}{d t} = \frac{P}{2} - 100 P e^{- 2 t}

P = e^{\frac{1}{2} (t + 100 e^{- 2 t}) + c_{1}}

Solution steps

\frac{d P}{d t} = \frac{P}{2} - 100 P e^{- 2 t}

Solve separable ODE:

P = e^{\frac{1}{2} (t + 100 e^{- 2 t}) + c_{1}}

P = e^{\frac{1}{2} (t + 100 e^{- 2 t}) + c_{1}}

What is the solution for (dP)/(dt)= P/2-100Pe^{-2t} ?
The solution for (dP)/(dt)= P/2-100Pe^{-2t} is P=e^{1/2 (t+100e^{-2t})+c_{1}}