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Beliebt Rechnen >

1/2 x^{''}+1/2 x^'-6x=10cos(3t)

Lösung

\frac{1}{2} x^{^{''}} + \frac{1}{2} x^{^{'}} - 6 x = 10 cos (3 t)

Lösung

x = c_{1} e^{3 t} + c_{2} e^{- 4 t} + \frac{2}{15} sin (3 t) - \frac{14}{15} cos (3 t)

Schritte zur Lösung

\frac{1}{2} x^{''} (t) + \frac{1}{2} x^{'} (t) - 6 x = 10 cos (3 t)

Solve linear ODE:

x = c_{1} e^{3 t} + c_{2} e^{- 4 t} + \frac{2}{15} sin (3 t) - \frac{14}{15} cos (3 t)

x = c_{1} e^{3 t} + c_{2} e^{- 4 t} + \frac{2}{15} sin (3 t) - \frac{14}{15} cos (3 t)

Graph

Beliebte Beispiele

y^{''}+4y^'+4y=4x+5

y^{^{''}} + 4 y^{^{'}} + 4 y = 4 x + 5

y^{''}+4y^'+4y=4x+6

y^{^{''}} + 4 y^{^{'}} + 4 y = 4 x + 6

y^{''}-2y^'-8y=-16t+16t^2

y^{^{''}} - 2 y^{^{'}} - 8 y = - 16 t + 16 t^{2}

y^{''}-16y=48t-24e^{-4t}

y^{^{''}} - 16 y = 48 t - 24 e^{- 4 t}

x^{''}+2x^'+50x=2cos(7t)

x^{^{''}} + 2 x^{^{'}} + 50 x = 2 cos (7 t)