y^{''''}-7y^{'''}+18y^{''}-20y^'+8y=0

Lösung

y^{^{''''}} - 7 y^{^{'''}} + 18 y^{^{''}} - 20 y^{^{'}} + 8 y = 0

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

Schritte zur Lösung

y^{(4)} (t) - 7 y^{'''} (t) + 18 y^{''} (t) - 20 y^{'} (t) + 8 y = 0

Solve linear ODE:

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

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

- y^{^{''}} - 2 \cdot π^{2} y = 0

y^{^{''}} + 64 y^{^{'}} + 16 y = 0

y^{^{''}} - 14 y^{^{'}} + 49 y = 0, y (0) = 0, y^{^{'}} (0) = 8

y^{^{''}} + 3 y^{^{'}} - 4 y = 0, y (0) = 0, y^{^{'}} (0) = 1

2 x^{^{''}} + 10 x = 0, x (0) = 1, x^{^{'}} (0) = - 2