(dx)/(dt)=50-(7x)/(100)

Lösung

\frac{d x}{d t} = 50 - \frac{7 x}{100}

x = - \frac{e ^{\frac{- 7 t - c _{1}}{100}}}{7} + \frac{5000}{7}

Schritte zur Lösung

\frac{d x}{d t} = 50 - \frac{7 x}{100}

Solve separable ODE:

x = - \frac{e ^{\frac{- 7 t - c _{1}}{100}}}{7} + \frac{5000}{7}

x = - \frac{e ^{\frac{- 7 t - c _{1}}{100}}}{7} + \frac{5000}{7}

(- y) d x + (x) d y = 0

y^{^{'}} + \frac{1}{2} y = 9

\frac{d y}{d x} = \frac{x}{y}, y (4) = - 3

\frac{d x}{d t} = x^{2} + (\frac{1}{81})

2 y^{^{'}} - 4 e^{2 x} y = 0, y (0) = 6