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Beliebt Rechnen >

y^{''}-y^'-12y=-5e^{3t},y(0)=0,y^'(0)=0

Lösung

y^{^{''}} - y^{^{'}} - 12 y = - 5 e^{3 t}, y (0) = 0, y^{^{'}} (0) = 0

Lösung

y = (\frac{5}{42} - \frac{5}{6}) e^{4 t} - \frac{5}{42} e^{- 3 t} + \frac{5}{6} e^{3 t}

Schritte zur Lösung

y^{''} (t) - y^{'} (t) - 12 y = - 5 e^{3 t}

Solve linear ODE:

y = (\frac{5}{42} - \frac{5}{6}) e^{4 t} - \frac{5}{42} e^{- 3 t} + \frac{5}{6} e^{3 t}

y = (\frac{5}{42} - \frac{5}{6}) e^{4 t} - \frac{5}{42} e^{- 3 t} + \frac{5}{6} e^{3 t}

Graph

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