(dP)/(dt)=-e^{-t}P,P(0)=100

Lösung

\frac{d P}{d t} = - e^{- t} P, P (0) = 100

P = 100 e^{e^{- t} - 1}

Schritte zur Lösung

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

Solve separable ODE:

P = 100 e^{e^{- t} - 1}

P = 100 e^{e^{- t} - 1}

y^{^{'}} = y^{\frac{1}{5}}

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

\frac{d y}{d x} y = arccos (\frac{1}{x})

y^{^{'}} - \frac{7}{5} y = 0

y^{^{'}} + y = y (t e^{t^{2}} + 1) t, y (0) = 1