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)

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)