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Beliebt Rechnen >

x^{''}+2x^'+41x=12cos(6t)

Lösung

x^{^{''}} + 2 x^{^{'}} + 41 x = 12 cos (6 t)

Lösung

x = e^{- t} (c_{1} cos (210 t) + c_{2} sin (210 t)) + \frac{144}{169} sin (6 t) + \frac{60}{169} cos (6 t)

Schritte zur Lösung

x^{''} (t) + 2 x^{'} (t) + 41 x = 12 cos (6 t)

Solve linear ODE:

x = e^{- t} (c_{1} cos (210 t) + c_{2} sin (210 t)) + \frac{144}{169} sin (6 t) + \frac{60}{169} cos (6 t)

x = e^{- t} (c_{1} cos (210 t) + c_{2} sin (210 t)) + \frac{144}{169} sin (6 t) + \frac{60}{169} cos (6 t)

Graph

Beliebte Beispiele

y^{''}+16y=4csc^2(4t)

y^{^{''}} + 16 y = 4 csc^{2} (4 t)

7y^{''}-20y^'+12y=8e^2

7 y^{^{''}} - 20 y^{^{'}} + 12 y = 8 e^{2}

y^{''}-2y^'+10y=18e^xsec(3x)

y^{^{''}} - 2 y^{^{'}} + 10 y = 18 e^{x} sec (3 x)

y^{''}+4y^'+4y=xe^{-x}

y^{^{''}} + 4 y^{^{'}} + 4 y = x e^{- x}

y^{''}-4y^'=64-6e^{-x}

y^{^{''}} - 4 y^{^{'}} = 64 - 6 e^{- x}