15y^{''''}+53y^{''}+16y=0

Lösung

15 y^{^{''''}} + 53 y^{^{''}} + 16 y = 0

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

Schritte zur Lösung

15 y^{(4)} (t) + 53 y^{''} (t) + 16 y = 0

Solve linear ODE:

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

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

2 y^{^{''}} - y^{^{'}} - 15 y = 0

y^{^{'''}} - 15 y^{^{''}} + 62 y^{^{'}} - 72 y = 0

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

y^{^{''}} + y^{^{'}} = 0, y (\frac{π}{3}) = 0, y^{^{'}} (\frac{π}{3}) = 2

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