(y^{''''}+8y^{''}+16y)^2=0

Lösung

(y^{^{''''}} + 8 y^{^{''}} + 16 y)^{2} = 0

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

Schritte zur Lösung

(y^{(4)} (t) + 8 y^{''} (t) + 16 y)^{2} = 0

Solve linear ODE:

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

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

y^{^{''}} + 5 y^{^{'}} + 4 y = 0, y (0) = 0, y^{^{'}} (0) = 1

y^{^{''}} + 6 y^{^{'}} + 9 y = 0, y (0) = 2, y^{^{'}} (0) = 1

y^{^{''}} + 6 y^{^{'}} + 9 y = 0, y (0) = 2, y^{^{'}} (0) = 0

y^{^{''}} - 4 y = 0, y^{0} = 0, y^{^{'}} 0 = 1

y^{^{''}} + 10 y^{^{'}} + 25 y = 0, y (0) = - 4, y^{^{'}} (0) = 16