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Beliebt Rechnen >

x^{''}+4x^'+8x=4e^{-2t}sin(2t)

Lösung

x^{^{''}} + 4 x^{^{'}} + 8 x = 4 e^{- 2 t} sin (2 t)

Lösung

x = e^{- 2 t} (c_{1} cos (2 t) + c_{2} sin (2 t)) - e^{- 2 t} t cos (2 t)

Schritte zur Lösung

x^{''} (t) + 4 x^{'} (t) + 8 x = 4 e^{- 2 t} sin (2 t)

Solve linear ODE:

x = e^{- 2 t} (c_{1} cos (2 t) + c_{2} sin (2 t)) - e^{- 2 t} t cos (2 t)

x = e^{- 2 t} (c_{1} cos (2 t) + c_{2} sin (2 t)) - e^{- 2 t} t cos (2 t)

Graph

Beliebte Beispiele

y^{''}-2y^'+10y=-sin(3t)

y^{^{''}} - 2 y^{^{'}} + 10 y = - sin (3 t)

y^{''''}+y^{''}=7x-3cos(x)

y^{^{''''}} + y^{^{''}} = 7 x - 3 cos (x)

2y^{'''}+3y^{''}-3y^'-2y=e^{-t}

2 y^{^{'''}} + 3 y^{^{''}} - 3 y^{^{'}} - 2 y = e^{- t}

y^{''}+6y^'+9y=(16e^{-3x})/(x^2+1)

y^{^{''}} + 6 y^{^{'}} + 9 y = \frac{16 e ^{- 3 x}}{x ^{2} + 1}

y^{''}-2y^'=30e^{-3t}

y^{^{''}} - 2 y^{^{'}} = 30 e^{- 3 t}