What is the solution for 10y^{''}+1000y=140cos(8t),y(0)=0,y^'(0)=0 ?

The solution for 10y^{''}+1000y=140cos(8t),y(0)=0,y^'(0)=0 is y= 7/18 cos(8t)-7/18 cos(10t)

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10y^{''}+1000y=140cos(8t),y(0)=0,y^'(0)=0

10 y^{^{''}} + 1000 y = 140 cos (8 t), y (0) = 0, y^{^{'}} (0) = 0

y = \frac{7}{18} cos (8 t) - \frac{7}{18} cos (10 t)

Solution steps

10 y^{''} (t) + 1000 y = 140 cos (8 t)

Solve linear ODE:

y = \frac{7}{18} cos (8 t) - \frac{7}{18} cos (10 t)

y = \frac{7}{18} cos (8 t) - \frac{7}{18} cos (10 t)

y^{^{''}} + 9 y = 2 t^{2} - 4, y (0) = 0, y^{^{'}} (0) = - 4

y^{^{''}} + 3 y^{^{'}} + 4 y = 2 sin (3 t)

y^{^{''}} + y^{^{'}} = 2 x + x

y^{^{''}} - 2 y^{^{'}} - 8 y = 2 e^{- 2 x} - e^{- x}

y^{^{''''}} - 16 y = 2 e^{- 2 x} + 3 e^{- 3 x} + cos (2 x) - 1

What is the solution for 10y^{''}+1000y=140cos(8t),y(0)=0,y^'(0)=0 ?
The solution for 10y^{''}+1000y=140cos(8t),y(0)=0,y^'(0)=0 is y= 7/18 cos(8t)-7/18 cos(10t)