y^{''''}+y=cos(x)

Lösung

y^{^{''''}} + y = cos (x)

y = e^{\frac{x}{2}} (c_{1} cos (\frac{x}{2}) + c_{2} sin (\frac{x}{2})) + e^{- \frac{x}{2}} (c_{3} cos (\frac{x}{2}) + c_{4} sin (\frac{x}{2})) + \frac{1}{2} cos (x)

Schritte zur Lösung

y^{(4)} (x) + y = cos (x)

Solve linear ODE:

y = e^{\frac{x}{2}} (c_{1} cos (\frac{x}{2}) + c_{2} sin (\frac{x}{2})) + e^{- \frac{x}{2}} (c_{3} cos (\frac{x}{2}) + c_{4} sin (\frac{x}{2})) + \frac{1}{2} cos (x)

y = e^{\frac{x}{2}} (c_{1} cos (\frac{x}{2}) + c_{2} sin (\frac{x}{2})) + e^{- \frac{x}{2}} (c_{3} cos (\frac{x}{2}) + c_{4} sin (\frac{x}{2})) + \frac{1}{2} cos (x)

y^{^{''}} - 4 y^{^{'}} + 5 y = 4 e^{3 t}, y (0) = 2, y^{^{'}} (0) = 7

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

x^{^{''}} + 3 x^{^{'}} + 2 x = sin (3 t)

x^{^{''}} + 8 x^{^{'}} + 16 = 0

x^{^{''''}} - x^{^{''}} = 1