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

Lösung

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

y = c_{1} + c_{2} t + e^{- \frac{t}{2}} (c_{3} cos (\frac{3 t}{2}) + c_{4} sin (\frac{3 t}{2}))

Schritte zur Lösung

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

Solve linear ODE:

y = c_{1} + c_{2} t + e^{- \frac{t}{2}} (c_{3} cos (\frac{3 t}{2}) + c_{4} sin (\frac{3 t}{2}))

y = c_{1} + c_{2} t + e^{- \frac{t}{2}} (c_{3} cos (\frac{3 t}{2}) + c_{4} sin (\frac{3 t}{2}))

y^{^{'''}} + 12 y^{^{''}} + 36 y^{^{'}} = 0

(d^{2} + 1)^{3} y = 0

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

y^{^{'''}} - 7 y^{^{'}} + 6 y = 0

(d^{3} - 3 d^{2} + 4) y = 0