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

解答

\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}}

求解步骤

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

求解可分离方程:

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

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

\frac{d y}{d x} = \frac{16 x}{e ^{y}}

\frac{d y}{d x} = \frac{x 4 - y ^{2}}{1 - x ^{2}}

u^{^{'}} = 2 e^{5 x - H (x)}

x^{^{'}} + (x - 25) + \frac{x - 25}{3} = 200

y^{^{'}} - 10 y + 25 y = 0