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Beliebt Rechnen >

y^{''}+6y^'+9=e^{4t},y(0)=0,y^'(0)=0

Lösung

y^{^{''}} + 6 y^{^{'}} + 9 = e^{4 t}, y (0) = 0, y^{^{'}} (0) = 0

Lösung

y = \frac{7}{30} - \frac{1}{40} - \frac{7}{30} e^{- 6 t} + \frac{1}{40} e^{4 t} - \frac{3 t}{2}

Schritte zur Lösung

y^{''} (t) + 6 y^{'} (t) + 9 = e^{4 t}

Solve linear ODE:

y = \frac{7}{30} - \frac{1}{40} - \frac{7}{30} e^{- 6 t} + \frac{1}{40} e^{4 t} - \frac{3 t}{2}

y = \frac{7}{30} - \frac{1}{40} - \frac{7}{30} e^{- 6 t} + \frac{1}{40} e^{4 t} - \frac{3 t}{2}

Graph

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