(d^3+6d^2+11d+6)y=0

Lösung

(d^{3} + 6 d^{2} + 11 d + 6) y = 0

y = c_{1} e^{- x} + c_{2} e^{- 2 x} + c_{3} e^{- 3 x}

Schritte zur Lösung

(d^{3} + 6 d^{2} + 11 d + 6) y = 0

Solve linear ODE:

y = c_{1} e^{- x} + c_{2} e^{- 2 x} + c_{3} e^{- 3 x}

y = c_{1} e^{- x} + c_{2} e^{- 2 x} + c_{3} e^{- 3 x}

y^{^{''}} + 3 y^{^{'}} - 10 y = 0, y (0) = 1, y^{^{'}} (0) = - 3

y^{^{''}} + 10 y^{^{'}} + 36 y = 0, y (0) = 1, y^{^{'}} (0) = 0

y^{^{''}} + 2 y^{^{'}} - 8 y = 0, y (0) = - 5, y^{^{'}} (0) = 26

(d^{5} - 6 d^{4} + 9 d^{3}) y = 0

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