(D^4+6D^3+9D^2)y=0

Lösung

(D^{4} + 6 D^{3} + 9 D^{2}) y = 0

y = c_{1} + c_{2} x + c_{3} e^{- 3 x} + c_{4} x e^{- 3 x}

Schritte zur Lösung

(D^{4} + 6 D^{3} + 9 D^{2}) y = 0

Solve linear ODE:

y = c_{1} + c_{2} x + c_{3} e^{- 3 x} + c_{4} x e^{- 3 x}

y = c_{1} + c_{2} x + c_{3} e^{- 3 x} + c_{4} x e^{- 3 x}

\frac{d ^{2} y}{d t ^{2}} - 6 \frac{d y}{d t} + 13 y = 0

2 y^{^{'''}} + y^{^{'}} = 0

y^{^{'''}} - 18 y^{^{''}} + 95 y^{^{'}} - 150 y = 0

\frac{d ^{2} y}{d x ^{2}} + 11 \frac{d y}{d x} + 28 y = 0

y^{^{''''}} + y^{^{'''}} - 5 y^{^{''}} - 3 y^{^{'}} + \frac{1}{2} y = 0