16y^{''''}=625y

Lösung

16 y^{^{''''}} = 625 y

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

Schritte zur Lösung

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

Solve linear ODE:

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

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

y^{^{''}} + 64 y = 0, y (0) = \frac{2}{3}, y^{^{'}} (0) = - \frac{4}{3}

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

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

y^{^{''}} + 4 y^{^{'}} + 29 y = 0, y (0) = 0, y^{^{'}} (0) = 5

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