y^{''''}+2y^{''}+y=9+cos(4t)

Lösung

y^{^{''''}} + 2 y^{^{''}} + y = 9 + cos (4 t)

y = c_{1} cos (t) + c_{2} sin (t) + t (c_{3} cos (t) + c_{4} sin (t)) + 9 + \frac{1}{225} cos (4 t)

Schritte zur Lösung

y^{(4)} (t) + 2 y^{''} (t) + y = 9 + cos (4 t)

Solve linear ODE:

y = c_{1} cos (t) + c_{2} sin (t) + t (c_{3} cos (t) + c_{4} sin (t)) + 9 + \frac{1}{225} cos (4 t)

y = c_{1} cos (t) + c_{2} sin (t) + t (c_{3} cos (t) + c_{4} sin (t)) + 9 + \frac{1}{225} cos (4 t)

y^{^{''}} + 10 y^{^{'}} + 16 y = 40 cos (4 t)

y^{^{''}} - 2 y^{^{'}} + y = \frac{13 e ^{t}}{1 + t ^{2}}

y^{^{''}} + 36 y = 7 sec (6 x)

y^{^{'''}} - y^{^{'}} = 2 sin (t)

y^{^{''}} - 4 y^{^{'}} + 4 y = t^{3} e^{2} t, y (0) = 0, y^{^{'}} (0) = 0