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

Lösung

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

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

Schritte zur Lösung

y^{(4)} (t) - y^{'''} (t) - 3 y^{''} (t) + 5 y^{'} (t) - 2 y = 0

Solve linear ODE:

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

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

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

9 y^{^{''}} + 12 y^{^{'}} + 29 y = 0

16 y^{^{''}} - 40 y^{^{'}} + 25 y = 0, y (0) = 3, y^{^{'}} (0) = - \frac{9}{4}

y^{^{''}} + 8 y^{^{'}} + 20 y = 0, y (0) = 2, y^{^{'}} (0) = - 7

\frac{d ^{2} y}{d x ^{2}} - 5 y = 0