y^{'''}+2y^{''}-5y^'-6y=sin(6t)

Lösung

y^{^{'''}} + 2 y^{^{''}} - 5 y^{^{'}} - 6 y = sin (6 t)

y = c_{1} e^{- t} + c_{2} e^{2 t} + c_{3} e^{- 3 t} - \frac{13}{11100} sin (6 t) + \frac{41}{11100} cos (6 t)

Schritte zur Lösung

y^{'''} (t) + 2 y^{''} (t) - 5 y^{'} (t) - 6 y = sin (6 t)

Solve linear ODE:

y = c_{1} e^{- t} + c_{2} e^{2 t} + c_{3} e^{- 3 t} - \frac{13}{11100} sin (6 t) + \frac{41}{11100} cos (6 t)

y = c_{1} e^{- t} + c_{2} e^{2 t} + c_{3} e^{- 3 t} - \frac{13}{11100} sin (6 t) + \frac{41}{11100} cos (6 t)

y^{^{''}} + 9 y = 7 sec (3 x)

y^{^{''}} - 36 y = - 42 e^{- 5 t}, y (0) = 7, y^{^{'}} (0) = 0

y^{^{''}} - 7 y^{^{'}} + 6 y = 2, y^{^{'}} (0) = 7

y^{^{'''}} - y^{^{'}} = 1 - x^{2}

y^{^{''}} - 4 y^{^{'}} + 3 y = 2 e^{(3 t)}