y^{''}+10y^'+16y=12cos(2x)+4sin(2x)

Lösung

y^{^{''}} + 10 y^{^{'}} + 16 y = 12 cos (2 x) + 4 sin (2 x)

y = c_{1} e^{- 2 x} + c_{2} e^{- 8 x} + \frac{9}{17} sin (2 x) + \frac{2}{17} cos (2 x)

Schritte zur Lösung

y^{''} (x) + 10 y^{'} (x) + 16 y = 12 cos (2 x) + 4 sin (2 x)

Solve linear ODE:

y = c_{1} e^{- 2 x} + c_{2} e^{- 8 x} + \frac{9}{17} sin (2 x) + \frac{2}{17} cos (2 x)

y = c_{1} e^{- 2 x} + c_{2} e^{- 8 x} + \frac{9}{17} sin (2 x) + \frac{2}{17} cos (2 x)

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

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

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

y^{^{''}} + 3 y^{^{'}} + 2 y = 2 x

y^{^{''}} + 6 y^{^{'}} + 5 y = 5 x^{3} + 13 x^{2} + 4 x