y^{''''}+2y^{''}+y=3+cos(5t)

Lösung

y^{^{''''}} + 2 y^{^{''}} + y = 3 + cos (5 t)

y = c_{1} cos (t) + c_{2} sin (t) + t (c_{3} cos (t) + c_{4} sin (t)) + 3 + \frac{1}{576} cos (5 t)

Schritte zur Lösung

y^{(4)} (t) + 2 y^{''} (t) + y = 3 + cos (5 t)

Solve linear ODE:

y = c_{1} cos (t) + c_{2} sin (t) + t (c_{3} cos (t) + c_{4} sin (t)) + 3 + \frac{1}{576} cos (5 t)

y = c_{1} cos (t) + c_{2} sin (t) + t (c_{3} cos (t) + c_{4} sin (t)) + 3 + \frac{1}{576} cos (5 t)

y^{^{''}} + y^{^{'}} - 2 y = 2 x, y (0) = 0, y^{^{'}} (0) = 1

y^{^{''}} - 8 y^{^{'}} + 16 y = 1 - x + e^{4 x}

y^{^{''}} - y^{^{'}} - 6 y = csc (x)

y^{^{'''}} - 2 y^{^{''}} - 5 y^{^{'}} + 6 y = e^{- 2 x}

y^{^{''}} - y = e^{x} + 2 e^{2 x}