(D^2+2D^2+D+2)y=0

Lösung

(D^{2} + 2 D^{2} + D + 2) y = 0

y = e^{- \frac{x}{6}} (c_{1} cos (\frac{23 x}{6}) + c_{2} sin (\frac{23 x}{6}))

Schritte zur Lösung

(D^{2} + 2 D^{2} + D + 2) y = 0

Solve linear ODE:

y = e^{- \frac{x}{6}} (c_{1} cos (\frac{23 x}{6}) + c_{2} sin (\frac{23 x}{6}))

y = e^{- \frac{x}{6}} (c_{1} cos (\frac{23 x}{6}) + c_{2} sin (\frac{23 x}{6}))

43 y^{^{'''}} - 13 y^{^{''}} + 42 y^{^{'}} = 0

y^{^{''}} - 5 y^{^{'}} - 6 y = 0, y (0) = 3, y^{^{'}} (0) = - 3

12 y^{^{''}} - 13 y^{^{'}} + y = 0, y (0) = 12, y^{^{'}} (0) = \frac{1}{12}

16 y^{^{''}} + 12 y^{^{'}} + 9 y = 0

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