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Beliebt Rechnen >

x^{''}-3x^'-4x=8e^tcos(2t)

Lösung

x^{^{''}} - 3 x^{^{'}} - 4 x = 8 e^{t} cos (2 t)

Lösung

x = c_{1} e^{4 t} + c_{2} e^{- t} - \frac{2}{13} e^{t} sin (2 t) - \frac{10}{13} e^{t} cos (2 t)

Schritte zur Lösung

x^{''} (t) - 3 x^{'} (t) - 4 x = 8 e^{t} cos (2 t)

Solve linear ODE:

x = c_{1} e^{4 t} + c_{2} e^{- t} - \frac{2}{13} e^{t} sin (2 t) - \frac{10}{13} e^{t} cos (2 t)

x = c_{1} e^{4 t} + c_{2} e^{- t} - \frac{2}{13} e^{t} sin (2 t) - \frac{10}{13} e^{t} cos (2 t)

Graph

Beliebte Beispiele

y^{'''}-3y^{''}-y^'+3y=e^{6x}

y^{^{'''}} - 3 y^{^{''}} - y^{^{'}} + 3 y = e^{6 x}

y^{''}-2y^'+y=t^{-1}e^t

y^{^{''}} - 2 y^{^{'}} + y = t^{- 1} e^{t}

y^{''}-11y^'+28y=216e^t

y^{^{''}} - 11 y^{^{'}} + 28 y = 216 e^{t}

y^{''}-6y^'+9y=4e^{-3t}

y^{^{''}} - 6 y^{^{'}} + 9 y = 4 e^{- 3 t}

y^{''}+5y^'+6y=sin(x)

y^{^{''}} + 5 y^{^{'}} + 6 y = sin (x)