y^{''}+3y^'+9y=8sin(6t)

Lösung

y^{^{''}} + 3 y^{^{'}} + 9 y = 8 sin (6 t)

y = e^{- \frac{3 t}{2}} (c_{1} cos (\frac{3 ^{\frac{3}{2}} t}{2}) + c_{2} sin (\frac{3 ^{\frac{3}{2}} t}{2})) - \frac{8}{39} sin (6 t) - \frac{16}{117} cos (6 t)

Schritte zur Lösung

y^{''} (t) + 3 y^{'} (t) + 9 y = 8 sin (6 t)

Solve linear ODE:

y = e^{- \frac{3 t}{2}} (c_{1} cos (\frac{3 ^{\frac{3}{2}} t}{2}) + c_{2} sin (\frac{3 ^{\frac{3}{2}} t}{2})) - \frac{8}{39} sin (6 t) - \frac{16}{117} cos (6 t)

y = e^{- \frac{3 t}{2}} (c_{1} cos (\frac{3 ^{\frac{3}{2}} t}{2}) + c_{2} sin (\frac{3 ^{\frac{3}{2}} t}{2})) - \frac{8}{39} sin (6 t) - \frac{16}{117} cos (6 t)

y^{^{''}} - y^{^{'}} + 0.25 y = 3 + e^{\frac{x}{2}}

y^{^{''}} + 2 y^{^{'}} - 3 y = 8 x e^{x}

10 y^{^{''}} + 1000 y = 140 cos (8 t), y (0) = 0, y^{^{'}} (0) = 0

y^{^{''}} + 9 y = 2 t^{2} - 4, y (0) = 0, y^{^{'}} (0) = - 4

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