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Beliebt Rechnen >

y^{''}+7y^'+12y=e^t,y(0)=0,y^'(0)=1

Lösung

y^{^{''}} + 7 y^{^{'}} + 12 y = e^{t}, y (0) = 0, y^{^{'}} (0) = 1

Lösung

y = (\frac{4}{5} - \frac{1}{20}) e^{- 3 t} - \frac{4}{5} e^{- 4 t} + \frac{1}{20} e^{t}

Schritte zur Lösung

y^{''} (t) + 7 y^{'} (t) + 12 y = e^{t}

Solve linear ODE:

y = (\frac{4}{5} - \frac{1}{20}) e^{- 3 t} - \frac{4}{5} e^{- 4 t} + \frac{1}{20} e^{t}

y = (\frac{4}{5} - \frac{1}{20}) e^{- 3 t} - \frac{4}{5} e^{- 4 t} + \frac{1}{20} e^{t}

Graph

Beliebte Beispiele

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

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

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)