55x^{''}+220x=0,x(0)=0,x^'(0)=-6

解

55 x^{^{''}} + 220 x = 0, x (0) = 0, x^{^{'}} (0) = - 6

x = - 3 sin (2 t)

解答ステップ

55 x^{''} (t) + 220 x = 0

線形 ODE を解く:

x = - 3 sin (2 t)

x = - 3 sin (2 t)

y^{^{'''}} + 3.1 y^{^{''}} + 3.1 y^{^{'}} + y = 0

y^{^{''}} + 6 y^{^{'}} + 8 y = 0, y (0) = \frac{2}{5}, y^{^{'}} (0) = \frac{2}{5}

y^{^{''}} + 20 y^{^{'}} + 36 y = 0, y^{^{'}} (0) = 0, y (0) = 5

- 2 y^{^{''}} + 8 y^{^{'}} = 0, y (- 1) = 2, y^{^{'}} (2) = 2

y^{^{''}} + 7 y^{^{'}} + 12 y = 0, y (0) = 1, y^{^{'}} (0) = 9