y^{''''}+3y^{'''}-y^{''}-3y^'+1/2 y=0

Lösung

y^{^{''''}} + 3 y^{^{'''}} - y^{^{''}} - 3 y^{^{'}} + \frac{1}{2} y = 0

y = c_{1} e^{0.16239 \dots t} + c_{2} e^{- 2.97867 \dots t} + c_{3} e^{0.92898 \dots t} + c_{4} e^{- 1.11269 \dots t}

Schritte zur Lösung

y^{(4)} (t) + 3 y^{'''} (t) - y^{''} (t) - 3 y^{'} (t) + \frac{1}{2} y = 0

Solve linear ODE:

y = c_{1} e^{0.16239 \dots t} + c_{2} e^{- 2.97867 \dots t} + c_{3} e^{0.92898 \dots t} + c_{4} e^{- 1.11269 \dots t}

y = c_{1} e^{0.16239 \dots t} + c_{2} e^{- 2.97867 \dots t} + c_{3} e^{0.92898 \dots t} + c_{4} e^{- 1.11269 \dots t}

64 y^{^{''}} - 144 y^{^{'}} + 81 y = 0

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

y^{^{''}} + 5 y^{^{'}} - 50 y = 0

y^{^{''}} - 440 y = 0

y^{^{''}} - 4 y^{^{'}} - 5 y = 0, y (- 1) = 3