y^'=3.2y-10y^2

Lösung

y^{^{'}} = 3.2 y - 10 y^{2}

y = - \frac{1.3914 E - 14 e ^{\frac{- t - c _{1}}{0.3125}}}{1 - e ^{\frac{- c _{1} - t}{0.3125}}} + \frac{0.32}{1 - e ^{\frac{- c _{1} - t}{0.3125}}}

Schritte zur Lösung

y^{'} (t) = 3.2 y - 10 y^{2}

Solve separable ODE:

y = - \frac{1.3914 E - 14 e ^{\frac{- t - c _{1}}{0.3125}}}{1 - e ^{\frac{- c _{1} - t}{0.3125}}} + \frac{0.32}{1 - e ^{\frac{- c _{1} - t}{0.3125}}}

y = - \frac{1.3914 E - 14 e ^{\frac{- t - c _{1}}{0.3125}}}{1 - e ^{\frac{- c _{1} - t}{0.3125}}} + \frac{0.32}{1 - e ^{\frac{- c _{1} - t}{0.3125}}}

y^{^{'}} = \frac{x ^{3}}{y ^{4}}

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

6 y \frac{d y}{d x} = 5 x^{2}

2 x y d x + 3 x^{2} d y = 0

\frac{d}{d x} (x^{2} + y^{2}) = 16