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Beliebt Rechnen >

(d^2y)/(dt^2)+2(dy)/(dt)+2y=cos(2t)

Lösung

\frac{d ^{2} y}{d t ^{2}} + 2 \frac{d y}{d t} + 2 y = cos (2 t)

Lösung

y = e^{- t} (c_{1} cos (t) + c_{2} sin (t)) + \frac{1}{5} sin (2 t) - \frac{1}{10} cos (2 t)

Schritte zur Lösung

\frac{d ^{2} y}{d t ^{2}} + 2 \frac{d y}{d t} + 2 y = cos (2 t)

Solve linear ODE:

y = e^{- t} (c_{1} cos (t) + c_{2} sin (t)) + \frac{1}{5} sin (2 t) - \frac{1}{10} cos (2 t)

y = e^{- t} (c_{1} cos (t) + c_{2} sin (t)) + \frac{1}{5} sin (2 t) - \frac{1}{10} cos (2 t)

Graph

Beliebte Beispiele

d er i v a t i v e 7 e

x*(dy)/(dx)=7xe^x-y+9x^2

x \cdot \frac{d y}{d x} = 7 x e^{x} - y + 9 x^{2}

integral of e^{3θ}sin(2θ)

\int e^{3 θ} sin (2 θ) d θ

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\int 1 + 4 θ^{2} d θ

laplacetransform e^{2t}(t-1)^2

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