(d^2x)/(dt^2)+324(dx)/(dt)+4x=0

Lösung

\frac{d ^{2} x}{d t ^{2}} + 324 \frac{d x}{d t} + 4 x = 0

x = c_{1} e^{2 (4410 - 81) t} + c_{2} e^{- 2 (81 + 4410) t}

Schritte zur Lösung

\frac{d ^{2} x}{d t ^{2}} + 324 \frac{d x}{d t} + 4 x = 0

Solve linear ODE:

x = c_{1} e^{2 (4410 - 81) t} + c_{2} e^{- 2 (81 + 4410) t}

x = c_{1} e^{2 (4410 - 81) t} + c_{2} e^{- 2 (81 + 4410) t}

x^{^{''}} + 5 \cdot x = 0

y^{^{''}} + 121 y = 0

2 y^{^{''}} + 4 y^{^{'}} + 8 y = 0

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

(4 D^{4} - 45 D^{2} - 70 D - 24) y = 0