What is the solution for 10y^{''}+1000y=100cos(8t),y(0)=0,y^'(0)=0 ?

The solution for 10y^{''}+1000y=100cos(8t),y(0)=0,y^'(0)=0 is y= 5/18 cos(8t)-5/18 cos(10t)

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10y^{''}+1000y=100cos(8t),y(0)=0,y^'(0)=0

10 y^{^{''}} + 1000 y = 100 cos (8 t), y (0) = 0, y^{^{'}} (0) = 0

y = \frac{5}{18} cos (8 t) - \frac{5}{18} cos (10 t)

Solution steps

10 y^{''} (t) + 1000 y = 100 cos (8 t)

Solve linear ODE:

y = \frac{5}{18} cos (8 t) - \frac{5}{18} cos (10 t)

y = \frac{5}{18} cos (8 t) - \frac{5}{18} cos (10 t)

y^{^{''}} + 9 y^{^{'}} + 14 y = 2 + t, y (0) = 1, y^{^{'}} (0) = 1

y^{^{'''}} - y^{^{''}} - y^{^{'}} + y = 9 e^{- t} + 3

y^{^{''}} + 10 y^{^{'}} + 25 y = 14 \cdot e^{- 5 x}

y^{^{'''}} - y^{^{''}} - y^{^{'}} + y = 9 e^{- t} + 6

y^{^{''}} = - 4 y^{^{'}} - 5 y + 2

What is the solution for 10y^{''}+1000y=100cos(8t),y(0)=0,y^'(0)=0 ?
The solution for 10y^{''}+1000y=100cos(8t),y(0)=0,y^'(0)=0 is y= 5/18 cos(8t)-5/18 cos(10t)