y^{''''}+2y^{''}+y=11+cos(3t)

Lösung

y^{^{''''}} + 2 y^{^{''}} + y = 11 + cos (3 t)

y = c_{1} cos (t) + c_{2} sin (t) + t (c_{3} cos (t) + c_{4} sin (t)) + 11 + \frac{1}{64} cos (3 t)

Schritte zur Lösung

y^{(4)} (t) + 2 y^{''} (t) + y = 11 + cos (3 t)

Solve linear ODE:

y = c_{1} cos (t) + c_{2} sin (t) + t (c_{3} cos (t) + c_{4} sin (t)) + 11 + \frac{1}{64} cos (3 t)

y = c_{1} cos (t) + c_{2} sin (t) + t (c_{3} cos (t) + c_{4} sin (t)) + 11 + \frac{1}{64} cos (3 t)

y^{^{''}} + 4 y = sin (3 t), y (0) = 1, y^{^{'}} (0) = 0

y^{^{''}} - 2 y^{^{'}} - 3 y = 12 e x - 6

y^{^{''}} - 2 y^{^{'}} - 3 y = 12 e x - 9

y^{^{''}} + 2 y^{^{'}} + 4 y = \frac{x}{e ^{2 x} ( 1 + x ^{2} )}

y^{^{''}} - y^{^{'}} + 64 y = 8 sin (8 t)