16y^{''}-8y^'+145y=0

Lösung

16 y^{^{''}} - 8 y^{^{'}} + 145 y = 0

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

Schritte zur Lösung

16 y^{''} (t) - 8 y^{'} (t) + 145 y = 0

Solve linear ODE:

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

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

y^{^{''''}} - 23 y^{^{''}} - 50 y = 0

y^{^{''}} + 5 y^{^{'}} + 4 y = 0, y (0) = 6, y^{^{'}} (0) = 2

4 y^{^{''}} - 8 y^{^{'}} + 3 y = 0, y (0) = 1, y^{^{'}} (0) = 2

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

y^{^{''}} + 2 y^{^{'}} + 5 y = 0, y (0) = 3, y^{^{'}} (0) = 5