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Beliebt Rechnen >

(dy)/(dt)=y^2e^{-t},y(0)= 1/2 ,t>= 0

Lösung

\frac{d y}{d t} = y^{2} e^{- t}, y (0) = \frac{1}{2}, t \geq 0

Lösung

y = \frac{e ^{t}}{1 + e ^{t}}

Schritte zur Lösung

\frac{d y}{d t} = y^{2} e^{- t}

Solve separable ODE:

y = \frac{e ^{t}}{1 + e ^{t}}

y = \frac{e ^{t}}{1 + e ^{t}}

Graph

Beliebte Beispiele

f(x)= 1/(1+x^2)f^'(x)

f (x) = \frac{1}{1 + x ^{2}} f^{^{'}} (x)

(dy)/(dx)=7xsec(y)

\frac{d y}{d x} = 7 x sec (y)

(dy)/(dx)=x^5(y-2),y(0)=6

\frac{d y}{d x} = x^{5} (y - 2), y (0) = 6

y^'+tan(2*x)y=0,y(0)=5

y^{^{'}} + tan (2 \cdot x) y = 0, y (0) = 5

V^'=4kpi(3/(4pi))^{2/3}V^{2/3}

V^{^{'}} = 4 kπ (\frac{3}{4 π})^{\frac{2}{3}} V^{\frac{2}{3}}