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Beliebt Rechnen >

(d^2y)/(dt^2)=1-e^{2t}

Lösung

\frac{d ^{2} y}{d t ^{2}} = 1 - e^{2 t}

Lösung

y = \frac{t ^{2}}{2} - \frac{1}{4} e^{2 t} + c_{1} t + c_{2}

Schritte zur Lösung

\frac{d ^{2} y}{d t ^{2}} = 1 - e^{2 t}

Ersetze

\frac{d ^{2} y}{d t ^{2}}

mit

y^{''} (t)

y^{^{''}} (t) = 1 - e^{2 t}

Löse

y^{''} (t) = 1 - e^{2 t} : y^{'} (t) = t - \frac{1}{2} e^{2 t} + c_{1}

Löse

y^{'} (t) = t - \frac{1}{2} e^{2 t} + c_{1} : y = \frac{t ^{2}}{2} - \frac{1}{4} e^{2 t} + c_{1} t + c_{2}

y = \frac{t ^{2}}{2} - \frac{1}{4} e^{2 t} + c_{1} t + c_{2}

Graph

Beliebte Beispiele

\frac{d}{d s} (ln (3))

integral of 1/(9+sqrt(2x))

\int \frac{1}{9 + 2 x} d x

fläche 2y=3sqrt(x),2y+3x=6,y=-3

a re a 2 y = 3 x, 2 y + 3 x = 6, y = - 3

derivative f(x)=(2x^2-5x)/(3x+5)

d er i v a t i v e f (x) = \frac{2 x ^{2} - 5 x}{3 x + 5}

integral from-5 to 5 of x

\int_{- 5}^{5} x d x