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Beliebt Rechnen >

y^{''}+4y^'+50y=65cos(2t)

Lösung

y^{^{''}} + 4 y^{^{'}} + 50 y = 65 cos (2 t)

Lösung

y = e^{- 2 t} (c_{1} cos (46 t) + c_{2} sin (46 t)) + \frac{26}{109} sin (2 t) + \frac{299}{218} cos (2 t)

Schritte zur Lösung

y^{''} (t) + 4 y^{'} (t) + 50 y = 65 cos (2 t)

Solve linear ODE:

y = e^{- 2 t} (c_{1} cos (46 t) + c_{2} sin (46 t)) + \frac{26}{109} sin (2 t) + \frac{299}{218} cos (2 t)

y = e^{- 2 t} (c_{1} cos (46 t) + c_{2} sin (46 t)) + \frac{26}{109} sin (2 t) + \frac{299}{218} cos (2 t)

Graph

Beliebte Beispiele

y^{''}-2y^'+y=e^xsec^2(x)

y^{^{''}} - 2 y^{^{'}} + y = e^{x} sec^{2} (x)

y^{''}-4y^'+4y=4(x+1)

y^{^{''}} - 4 y^{^{'}} + 4 y = 4 (x + 1)

y^{''}-6y+9y=e^{-2x}sin(3x)

y^{^{''}} - 6 y + 9 y = e^{- 2 x} sin (3 x)

y^{''}-y^'+2y=3sin(3x)

y^{^{''}} - y^{^{'}} + 2 y = 3 sin (3 x)

y^{''''}+2y^{''}+y=9t+6

y^{^{''''}} + 2 y^{^{''}} + y = 9 t + 6