(dv)/(dt)=8-7v

Lösung

\frac{d v}{d t} = 8 - 7 v

v = - \frac{e ^{- 7 t - c_{1}}}{7} + \frac{8}{7}

Schritte zur Lösung

\frac{d v}{d t} = 8 - 7 v

Solve separable ODE:

v = - \frac{e ^{- 7 t - c_{1}}}{7} + \frac{8}{7}

v = - \frac{e ^{- 7 t - c_{1}}}{7} + \frac{8}{7}

x y^{^{'}} = (x - 1) y

\frac{d v}{d x} = \frac{e ^{v}}{x}

\frac{d y}{d x} = \frac{x cos ( x )}{y}

x^{^{'}} = 2 t x + t

y^{^{'}} = \frac{5 x ^{2} - 1}{5 + 7 y}