y^{''''}+2y^{''}+y=5+cos(4t)

Lösung

y^{^{''''}} + 2 y^{^{''}} + y = 5 + cos (4 t)

y = c_{1} cos (t) + c_{2} sin (t) + t (c_{3} cos (t) + c_{4} sin (t)) + 5 + \frac{1}{225} cos (4 t)

Schritte zur Lösung

y^{(4)} (t) + 2 y^{''} (t) + y = 5 + cos (4 t)

Solve linear ODE:

y = c_{1} cos (t) + c_{2} sin (t) + t (c_{3} cos (t) + c_{4} sin (t)) + 5 + \frac{1}{225} cos (4 t)

y = c_{1} cos (t) + c_{2} sin (t) + t (c_{3} cos (t) + c_{4} sin (t)) + 5 + \frac{1}{225} cos (4 t)

4 y^{^{''}} - 16 y = 1

\frac{d ^{2} y}{d x ^{2}} + y = e^{x}, y (0) = 0, y^{^{'}} (0) = 0

y^{^{''}} + y = t, y (0) = 1, y^{^{'}} (0) = - 2

y^{^{''''}} + 2 y^{^{''}} + y = 5 + cos (5 t)

y^{^{''}} - 2 y^{^{'}} - 48 y = - 136 t + 96 t^{2}