(d^6-4d^4+4d^2)*y=0

Lösung

(d^{6} - 4 d^{4} + 4 d^{2}) \cdot y = 0

y = c_{1} + c_{2} x + c_{3} e^{2 x} + c_{4} x e^{2 x} + c_{5} e^{- 2 x} + c_{6} x e^{- 2 x}

Schritte zur Lösung

(d^{6} - 4 d^{4} + 4 d^{2}) y = 0

Solve linear ODE:

y = c_{1} + c_{2} x + c_{3} e^{2 x} + c_{4} x e^{2 x} + c_{5} e^{- 2 x} + c_{6} x e^{- 2 x}

y = c_{1} + c_{2} x + c_{3} e^{2 x} + c_{4} x e^{2 x} + c_{5} e^{- 2 x} + c_{6} x e^{- 2 x}

4 y^{^{'''}} - 12 y^{^{'}} + 9 y^{^{'}} = 0

y^{^{''}} - y^{^{'}} - 5 y = 0

\frac{5}{8} x^{^{''}} + 80 x = 0

\frac{d ^{2} x}{d t ^{2}} = - 4 x

\frac{d ^{2} y}{d x ^{2}} + 8 \frac{d y}{d x} + 12 y = 0