15y^{''''}+32y^{''}+9y=0

Lösung

15 y^{^{''''}} + 32 y^{^{''}} + 9 y = 0

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

Schritte zur Lösung

15 y^{(4)} (t) + 32 y^{''} (t) + 9 y = 0

Solve linear ODE:

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

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

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

y^{^{''}} + 4 y^{^{'}} - 5 y = 0, y (0) = 2, y^{^{'}} (0) = 14

33 y^{^{''''}} - 188 y^{^{''}} + 64 y = 0

y^{^{''}} + 3 y^{^{'}} - 18 y = 0, y (0) = a, y^{^{'}} (0) = - 12

(4 D^{2} - 4 D + 1) y = 0