y^'=0.008y+40,y(0)=0

Lösung

y^{^{'}} = 0.008 y + 40, y (0) = 0

y = 5000 e^{\frac{t}{125}} - 5000

Schritte zur Lösung

y^{'} (t) = 0.008 y + 40

Solve separable ODE:

y = 5000 e^{\frac{t}{125}} - 5000

y = 5000 e^{\frac{t}{125}} - 5000

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

x \cdot y \cdot d x + (1 + x^{2}) d y = 0

(x^{2} + C) d x + x y d y = 0

x^{^{'}} = 3 x^{\frac{2}{3}}

\frac{d y}{d x} = \frac{2 x ^{4}}{y}