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

Lösung

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

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

Schritte zur Lösung

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

Solve linear ODE:

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

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

y^{^{''}} + 4 y = g (t), y (0) = 4, y^{^{'}} (0) = 0

y^{^{''}} - 3 + y^{^{'}} + 2 y = 0

y^{^{''}} - 4 y = 4 x

y^{^{''}} + 3 y = - 48 t^{2} e^{3} t

y^{^{''''}} - 256 y = 2 e^{- 4 x} + 3 e^{3 x} + cos (4 x) + 2