x^{''}+4x^'+40x=20sin(6t)

Lösung

x^{^{''}} + 4 x^{^{'}} + 40 x = 20 sin (6 t)

x = e^{- 2 t} (c_{1} cos (6 t) + c_{2} sin (6 t)) + \frac{5}{37} sin (6 t) - \frac{30}{37} cos (6 t)

Schritte zur Lösung

x^{''} (t) + 4 x^{'} (t) + 40 x = 20 sin (6 t)

Solve linear ODE:

x = e^{- 2 t} (c_{1} cos (6 t) + c_{2} sin (6 t)) + \frac{5}{37} sin (6 t) - \frac{30}{37} cos (6 t)

x = e^{- 2 t} (c_{1} cos (6 t) + c_{2} sin (6 t)) + \frac{5}{37} sin (6 t) - \frac{30}{37} cos (6 t)

y^{^{''}} - y^{^{'}} = 3

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

6 \frac{d ^{2} y}{d x ^{2}} + 4 \frac{d y}{d x} - 2 y = 3 x - 2

y^{^{''}} + 4 y^{^{'}} + 5 y = t

y^{^{''}} - y^{^{'}} - 2 y = 4 x e^{3 x}