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

Lösung

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

y = c_{1} e^{- 2 t} + c_{2} e^{- 3 t} + \frac{1}{10} sin (t) - \frac{1}{10} cos (t) - \frac{5}{52} sin (2 t) - \frac{1}{52} cos (2 t)

Schritte zur Lösung

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

Solve linear ODE:

y = c_{1} e^{- 2 t} + c_{2} e^{- 3 t} + \frac{1}{10} sin (t) - \frac{1}{10} cos (t) - \frac{5}{52} sin (2 t) - \frac{1}{52} cos (2 t)

y = c_{1} e^{- 2 t} + c_{2} e^{- 3 t} + \frac{1}{10} sin (t) - \frac{1}{10} cos (t) - \frac{5}{52} sin (2 t) - \frac{1}{52} cos (2 t)

y^{^{''}} + 7 y^{^{'}} + 6 y = e^{2 t}

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

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

y^{^{''}} + y = e^{- x} (2 sin (x) + 4 cos (x))

y^{^{''}} + y^{^{'}} - 7 y = 3 e^{2 x} - 2 e^{3 x}