(dP)/(dt)P=(5000(2)^{-t/(10)})

Lösung

\frac{d P}{d t} P = (5000 (2)^{- \frac{t}{10}})

P = \frac{- 3125 \cdot 2 ^{\frac{- t + 50}{10}} + c _{1}}{ln ( 2 )}, P = - \frac{- 3125 \cdot 2 ^{\frac{- t + 50}{10}} + c _{1}}{ln ( 2 )}

Schritte zur Lösung

\frac{d P}{d t} P = (5000 (2)^{- \frac{t}{10}})

Solve separable ODE:

P = \frac{- 3125 \cdot 2 ^{\frac{- t + 50}{10}} + c _{1}}{ln ( 2 )}, P = - \frac{- 3125 \cdot 2 ^{\frac{- t + 50}{10}} + c _{1}}{ln ( 2 )}

P = \frac{- 3125 \cdot 2 ^{\frac{- t + 50}{10}} + c _{1}}{ln ( 2 )}, P = - \frac{- 3125 \cdot 2 ^{\frac{- t + 50}{10}} + c _{1}}{ln ( 2 )}

y + y^{^{'}} x = 0

y^{^{'}} = 5 x y^{6}

7 y d y = \frac{3}{x} d x

x^{2} + 6 d x - \frac{1}{x csc ( - 8 y )} d y = 0

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