y^{''}-y^'-6y=73cos(3x)

Lösung

y^{^{''}} - y^{^{'}} - 6 y = 73 cos (3 x)

y = c_{1} e^{3 x} + c_{2} e^{- 2 x} - \frac{73}{78} sin (3 x) - \frac{365}{78} cos (3 x)

Schritte zur Lösung

y^{''} (x) - y^{'} (x) - 6 y = 73 cos (3 x)

Solve linear ODE:

y = c_{1} e^{3 x} + c_{2} e^{- 2 x} - \frac{73}{78} sin (3 x) - \frac{365}{78} cos (3 x)

y = c_{1} e^{3 x} + c_{2} e^{- 2 x} - \frac{73}{78} sin (3 x) - \frac{365}{78} cos (3 x)

y^{^{'''}} + y^{^{''}} + y^{^{'}} + y = e^{- t} + 8 t

y^{^{'''}} + y^{^{''}} + y^{^{'}} + y = e^{- t} + 7 t

y^{^{''}} - 2 y^{^{'}} + y = 6 t - 2, y (- 1) = 3, y^{^{'}} (- 1) = 7

y^{^{''}} + 4 y^{^{'}} + y = 4, y (0) = 0, y^{^{'}} (0) = 1

y^{^{''}} - 4 y^{^{'}} + 5 y = e^{2 x} (sin (x) + 2 cos (x))