(dx)/(dt)=t^3(1-x),x(0)=3

Lösung

\frac{d x}{d t} = t^{3} (1 - x), x (0) = 3

x = 1 + \frac{2}{e ^{\frac{t ^{4}}{4}}}

Schritte zur Lösung

\frac{d x}{d t} = t^{3} (1 - x)

Solve linear ODE:

x = 1 + \frac{2}{e ^{\frac{t ^{4}}{4}}}

x = 1 + \frac{2}{e ^{\frac{t ^{4}}{4}}}

\frac{d}{d x} (3 x^{k - 2} + 2 k x^{k - 1} + 4 x^{k})

\int \frac{x}{( x - 2 ) ^{3}} d x

\frac{d}{d x} (\frac{1}{4} e^{x} + \frac{3}{4} e^{- x})

\frac{d}{d x} (\frac{1 + x ^{2}}{x})

x \to 4 lim (\frac{6}{x})