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Beliebt Rechnen >

y^{''}+2y^'+5y=4sin(2t)

Lösung

y^{^{''}} + 2 y^{^{'}} + 5 y = 4 sin (2 t)

Lösung

y = e^{- t} (c_{1} cos (2 t) + c_{2} sin (2 t)) + \frac{4}{17} sin (2 t) - \frac{16}{17} cos (2 t)

Schritte zur Lösung

y^{''} (t) + 2 y^{'} (t) + 5 y = 4 sin (2 t)

Solve linear ODE:

y = e^{- t} (c_{1} cos (2 t) + c_{2} sin (2 t)) + \frac{4}{17} sin (2 t) - \frac{16}{17} cos (2 t)

y = e^{- t} (c_{1} cos (2 t) + c_{2} sin (2 t)) + \frac{4}{17} sin (2 t) - \frac{16}{17} cos (2 t)

Graph

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