y^'=0.23y-0.0005y^2

Lösung

y^{^{'}} = 0.23 y - 0.0005 y^{2}

y = - \frac{2.23607 E - 11 e ^{- 0.23 t - 0.23 c_{1}}}{1 - e ^{- 0.23 (t + c_{1})}} + \frac{459.99999 \dots}{1 - e ^{- 0.23 (t + c_{1})}}

Schritte zur Lösung

y^{'} (t) = 0.23 y - 0.0005 y^{2}

Solve separable ODE:

y = - \frac{2.23607 E - 11 e ^{- 0.23 t - 0.23 c_{1}}}{1 - e ^{- 0.23 (t + c_{1})}} + \frac{459.99999 \dots}{1 - e ^{- 0.23 (t + c_{1})}}

y = - \frac{2.23607 E - 11 e ^{- 0.23 t - 0.23 c_{1}}}{1 - e ^{- 0.23 (t + c_{1})}} + \frac{459.99999 \dots}{1 - e ^{- 0.23 (t + c_{1})}}

\int_{0}^{60} (60 - y)^{2} d y

x y^{^{'}} + y = 3 x y

\int_{1}^{10} \frac{1}{x ^{2}} d x

d er i v a t i v e x^{2} (sin (x))

\frac{d y}{d x} = y \cdot (\frac{1}{x} - y)