y^{''''}-4y^{'''}+8y^{''}-16y^'+16y=0

Lösung

y^{^{''''}} - 4 y^{^{'''}} + 8 y^{^{''}} - 16 y^{^{'}} + 16 y = 0

y = c_{1} e^{2 t} + c_{2} t e^{2 t} + c_{3} cos (2 t) + c_{4} sin (2 t)

Schritte zur Lösung

y^{(4)} (t) - 4 y^{'''} (t) + 8 y^{''} (t) - 16 y^{'} (t) + 16 y = 0

Solve linear ODE:

y = c_{1} e^{2 t} + c_{2} t e^{2 t} + c_{3} cos (2 t) + c_{4} sin (2 t)

y = c_{1} e^{2 t} + c_{2} t e^{2 t} + c_{3} cos (2 t) + c_{4} sin (2 t)

y^{^{''}} + 2 y^{^{'}} + 5 y = 0, y (0) = 3, y^{^{'}} (0) = - 2

2 y^{^{''}} - 2 y^{^{'}} + y = 0, y (0) = - 1, y^{^{'}} (0) = 2

y^{^{''}} + 4 y^{^{'}} + 2 y = 0, y (0) = 0, y^{^{'}} (0) = 1

\frac{d ^{2} y}{d t ^{2}} + 16 y = 0

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