What is the solution for 10y^{''}+1000y=160cos(8t) ?

The solution for 10y^{''}+1000y=160cos(8t) is y=c_{1}cos(10t)+c_{2}sin(10t)+4/9 cos(8t)

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10y^{''}+1000y=160cos(8t)

10 y^{^{''}} + 1000 y = 160 cos (8 t)

y = c_{1} cos (10 t) + c_{2} sin (10 t) + \frac{4}{9} cos (8 t)

Solution steps

10 y^{''} (t) + 1000 y = 160 cos (8 t)

Solve linear ODE:

y = c_{1} cos (10 t) + c_{2} sin (10 t) + \frac{4}{9} cos (8 t)

y = c_{1} cos (10 t) + c_{2} sin (10 t) + \frac{4}{9} cos (8 t)

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

y^{^{''}} + y^{^{'}} - 2 y = 13 + e^{x}

y^{^{''}} - 4 y^{^{'}} + 4 y = 3 x e^{2 x}

y^{^{''}} - 3 y^{^{'}} - 4 y = 4 t^{2} - 1

y^{^{''}} + 11 y^{^{'}} + 24 y = 4 sin (4 t) + 2 e^{- 8 t}

What is the solution for 10y^{''}+1000y=160cos(8t) ?
The solution for 10y^{''}+1000y=160cos(8t) is y=c_{1}cos(10t)+c_{2}sin(10t)+4/9 cos(8t)