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Beliebt Rechnen >

y^{'''}-2y^{''}-y^'+2y=e^{7t}

Lösung

y^{^{'''}} - 2 y^{^{''}} - y^{^{'}} + 2 y = e^{7 t}

Lösung

y = c_{1} e^{2 t} + c_{2} e^{- t} + c_{3} e^{t} + \frac{1}{240} e^{7 t}

Schritte zur Lösung

y^{'''} (t) - 2 y^{''} (t) - y^{'} (t) + 2 y = e^{7 t}

Solve linear ODE:

y = c_{1} e^{2 t} + c_{2} e^{- t} + c_{3} e^{t} + \frac{1}{240} e^{7 t}

y = c_{1} e^{2 t} + c_{2} e^{- t} + c_{3} e^{t} + \frac{1}{240} e^{7 t}

Graph

Beliebte Beispiele

y^{''}+3y^'-18y=-66t+36t^2

y^{^{''}} + 3 y^{^{'}} - 18 y = - 66 t + 36 t^{2}

y^{''}+3y^'+2y=4x^2

y^{^{''}} + 3 y^{^{'}} + 2 y = 4 x^{2}

y^{''}+2y^'+5y=3e^{-2t}

y^{^{''}} + 2 y^{^{'}} + 5 y = 3 e^{- 2 t}

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

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

y^{''}+4y^'+4y=7e^{-2t}

y^{^{''}} + 4 y^{^{'}} + 4 y = 7 e^{- 2 t}