256y^{''''}=625y

Lösung

256 y^{^{''''}} = 625 y

y = c_{1} e^{\frac{5 t}{4}} + c_{2} e^{- \frac{5 t}{4}} + c_{3} cos (\frac{5 t}{4}) + c_{4} sin (\frac{5 t}{4})

Schritte zur Lösung

256 y^{(4)} (t) = 625 y

Solve linear ODE:

y = c_{1} e^{\frac{5 t}{4}} + c_{2} e^{- \frac{5 t}{4}} + c_{3} cos (\frac{5 t}{4}) + c_{4} sin (\frac{5 t}{4})

y = c_{1} e^{\frac{5 t}{4}} + c_{2} e^{- \frac{5 t}{4}} + c_{3} cos (\frac{5 t}{4}) + c_{4} sin (\frac{5 t}{4})

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

y^{^{''''}} - 7 y^{^{'''}} + 17 y^{^{''}} - 17 y^{^{'}} + 6 y = 0

4 y^{^{''}} + 20 y^{^{'}} + 29 y = 0, y (0) = 8

9 y^{^{''}} + 24 y^{^{'}} - 33 y = 0

y^{^{''}} + 6 y^{^{'}} + 13 y = 0, y (0) = 3, y^{^{'}} (0) = 1