What is the solution for 10y^{''}+1000y=50cos(8t) ?

The solution for 10y^{''}+1000y=50cos(8t) is y=c_{1}cos(10t)+c_{2}sin(10t)+5/36 cos(8t)

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10y^{''}+1000y=50cos(8t)

10 y^{^{''}} + 1000 y = 50 cos (8 t)

y = c_{1} cos (10 t) + c_{2} sin (10 t) + \frac{5}{36} cos (8 t)

Solution steps

10 y^{''} (t) + 1000 y = 50 cos (8 t)

Solve linear ODE:

y = c_{1} cos (10 t) + c_{2} sin (10 t) + \frac{5}{36} cos (8 t)

y = c_{1} cos (10 t) + c_{2} sin (10 t) + \frac{5}{36} cos (8 t)

\frac{d}{d x} (e^{- x} (1 - x))

3 π r^{2}

\frac{d}{d x} (x^{2} e^{- 0.04 x})

\frac{\partial}{\partial y} (x e^{- 2 x})

\frac{\partial}{\partial x} (x y^{2} z)

What is the solution for 10y^{''}+1000y=50cos(8t) ?
The solution for 10y^{''}+1000y=50cos(8t) is y=c_{1}cos(10t)+c_{2}sin(10t)+5/36 cos(8t)