y^{''}-8y^'+80y=-2sin(3t)

Lösung

y^{^{''}} - 8 y^{^{'}} + 80 y = - 2 sin (3 t)

y = e^{4 t} (c_{1} cos (8 t) + c_{2} sin (8 t)) - \frac{142}{5617} sin (3 t) - \frac{48}{5617} cos (3 t)

Schritte zur Lösung

y^{''} (t) - 8 y^{'} (t) + 80 y = - 2 sin (3 t)

Solve linear ODE:

y = e^{4 t} (c_{1} cos (8 t) + c_{2} sin (8 t)) - \frac{142}{5617} sin (3 t) - \frac{48}{5617} cos (3 t)

y = e^{4 t} (c_{1} cos (8 t) + c_{2} sin (8 t)) - \frac{142}{5617} sin (3 t) - \frac{48}{5617} cos (3 t)

0.25 y^{^{''}} + 0.25 y^{^{'}} + 16 y = 3 cos (2 t)

y^{^{''}} - 4 y^{^{'}} + 40 y = t e^{2 t} sin (6 t)

y^{^{''}} + 3 y^{^{'}} - 7 y = t^{4} e^{t}

x^{^{''}} - 16 x^{^{'}} + 64 x = t e^{8 t}

0.5 y^{^{''}} + 5 y^{^{'}} + 12 y = e^{- 4 t} (4 t - 2)