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

Lösung

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

y = c_{1} e^{0.21830 \dots t} + c_{2} e^{0.78399 \dots t} + c_{3} e^{- 1.85844 \dots t} + c_{4} e^{- 3.14386 \dots t}

Schritte zur Lösung

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

Solve linear ODE:

y = c_{1} e^{0.21830 \dots t} + c_{2} e^{0.78399 \dots t} + c_{3} e^{- 1.85844 \dots t} + c_{4} e^{- 3.14386 \dots t}

y = c_{1} e^{0.21830 \dots t} + c_{2} e^{0.78399 \dots t} + c_{3} e^{- 1.85844 \dots t} + c_{4} e^{- 3.14386 \dots t}

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

x^{^{''}} + 2 x^{^{'}} + 1^{2} x = 0

y^{^{''}} + 3 y^{^{'}} - 4 y = 0, y (0) = 5, y^{^{'}} (0) = 10

x^{^{''}} - 2 x^{^{'}} + 3 x = 0

2 y^{^{''}} + 5 y^{^{'}} - 3 y = 0, y (0) = 5, y^{^{'}} (0) = 13