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Beliebt Rechnen >

3y^{''}+12y^'+39y=90sin(3t)

Lösung

3 y^{^{''}} + 12 y^{^{'}} + 39 y = 90 sin (3 t)

Lösung

y = e^{- 2 t} (c_{1} cos (3 t) + c_{2} sin (3 t)) + \frac{3}{4} sin (3 t) - \frac{9}{4} cos (3 t)

Schritte zur Lösung

3 y^{''} (t) + 12 y^{'} (t) + 39 y = 90 sin (3 t)

Solve linear ODE:

y = e^{- 2 t} (c_{1} cos (3 t) + c_{2} sin (3 t)) + \frac{3}{4} sin (3 t) - \frac{9}{4} cos (3 t)

y = e^{- 2 t} (c_{1} cos (3 t) + c_{2} sin (3 t)) + \frac{3}{4} sin (3 t) - \frac{9}{4} cos (3 t)

Graph

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