x^{'''}-4x^{''}-3x^'+18x=0

Lösung

x^{^{'''}} - 4 x^{^{''}} - 3 x^{^{'}} + 18 x = 0

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

Schritte zur Lösung

x^{'''} (t) - 4 x^{''} (t) - 3 x^{'} (t) + 18 x = 0

Solve linear ODE:

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

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

4 y^{^{''}} - 4 y^{^{'}} + 5 y = 0

y^{^{''}} - 10 y^{^{'}} - y = 0

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

x^{^{''}} - x^{^{'}} - 6 x = 0

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