y^'=y(0.1-10^{-7}y)

Lösung

y^{^{'}} = y (0.1 - 1 0^{- 7} y)

y = \frac{0.1 e ^{\frac{t + c _{1}}{10}}}{0.0000001 ( - 1 + e ^{\frac{c _{1} + t}{10}} )}

Schritte zur Lösung

y^{'} (t) = y (0.1 - 1 0^{- 7} y)

Solve separable ODE:

y = \frac{0.1 e ^{\frac{t + c _{1}}{10}}}{0.0000001 ( - 1 + e ^{\frac{c _{1} + t}{10}} )}

y = \frac{0.1 e ^{\frac{t + c _{1}}{10}}}{0.0000001 ( - 1 + e ^{\frac{c _{1} + t}{10}} )}

x y^{^{'}} + y = y^{- 8}

y^{^{'}} cos (x) - 2 y sin (x) = 0

\frac{d y}{d t} = 0.1 y, y (0) = 350

y^{^{'}} - \frac{2}{x} y = - \frac{2}{x}

3 y \frac{d y}{d t} + \frac{1}{y} = 0