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Beliebt Rechnen >

x^{''}+5x^'+4x=12.5cos(4t)

Lösung

x^{^{''}} + 5 x^{^{'}} + 4 x = 12.5 cos (4 t)

Lösung

x = c_{1} e^{- t} + c_{2} e^{- 4 t} + 0.45955 \dots sin (4 t) - \frac{75}{272} cos (4 t)

Schritte zur Lösung

x^{''} (t) + 5 x^{'} (t) + 4 x = 12.5 cos (4 t)

Solve linear ODE:

x = c_{1} e^{- t} + c_{2} e^{- 4 t} + 0.45955 \dots sin (4 t) - \frac{75}{272} cos (4 t)

x = c_{1} e^{- t} + c_{2} e^{- 4 t} + 0.45955 \dots sin (4 t) - \frac{75}{272} cos (4 t)

Graph

Beliebte Beispiele

x^{''}-4x^'+4x=4e^{2t}

x^{^{''}} - 4 x^{^{'}} + 4 x = 4 e^{2 t}

y^{''}-4y=2e^{4t}

y^{^{''}} - 4 y = 2 e^{4 t}

y^{''}-6y^'+9y=25e^tsin(t)

y^{^{''}} - 6 y^{^{'}} + 9 y = 25 e^{t} sin (t)

(D^2+7D+6)y=e^{2x}

(D^{2} + 7 D + 6) y = e^{2 x}

y^{''}=2y+18tan^3(x)

y^{^{''}} = 2 y + 18 tan^{3} (x)