(d^3-3d^2+4)y=0

Lösung

(d^{3} - 3 d^{2} + 4) y = 0

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

Schritte zur Lösung

(d^{3} - 3 d^{2} + 4) y = 0

Solve linear ODE:

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

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

10 y^{^{''}} - 32 y^{^{'}} + 25.6 y = 0

(d^{2} + d) \cdot y = 0

(d^{3} - 1) \cdot y = 0

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

(d^{5} + 2 d^{3} + d) y = 0