x^{''}+200x^'+100000x=100sin(100t)

Lösung

x^{^{''}} + 200 x^{^{'}} + 100000 x = 100 sin (100 t)

x = e^{- 100 t} (c_{1} cos (300 t) + c_{2} sin (300 t)) + \frac{9}{8500} sin (100 t) - \frac{1}{4250} cos (100 t)

Schritte zur Lösung

x^{''} (t) + 200 x^{'} (t) + 100000 x = 100 sin (100 t)

Solve linear ODE:

x = e^{- 100 t} (c_{1} cos (300 t) + c_{2} sin (300 t)) + \frac{9}{8500} sin (100 t) - \frac{1}{4250} cos (100 t)

x = e^{- 100 t} (c_{1} cos (300 t) + c_{2} sin (300 t)) + \frac{9}{8500} sin (100 t) - \frac{1}{4250} cos (100 t)

2 y^{^{''}} + 6 y^{^{'}} + 10 y = 4 cos (t)

y^{^{''}} - 14 y^{^{'}} + 49 y = 2 x e^{7 x}

y^{^{''}} - 6 y^{^{'}} + 9 y = e^{3} x, y (0) = - 1, y^{^{'}} (0) = 1

\frac{d ^{2} y}{d t ^{2}} - 5 \frac{d y}{d t} + 6 = 0

- 5 y^{^{''}} - 2 y^{^{'}} + 24 = 0