What is the solution for 55x^{''}+220x=0,x(0)=0,x^'(0)=-6 ?

The solution for 55x^{''}+220x=0,x(0)=0,x^'(0)=-6 is x=-3sin(2t)

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

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

x = - 3 sin (2 t)

Solution steps

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

Solve linear ODE:

x = - 3 sin (2 t)

x = - 3 sin (2 t)

y^{^{''}} + 2 y^{^{'}} - 8 y = 0, y (0) = 3, y^{^{'}} (0) = 12

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

What is the solution for 55x^{''}+220x=0,x(0)=0,x^'(0)=-6 ?
The solution for 55x^{''}+220x=0,x(0)=0,x^'(0)=-6 is x=-3sin(2t)