What is the solution for 10y^{''}+1000y=80cos(8t) ?

The solution for 10y^{''}+1000y=80cos(8t) is y=c_{1}cos(10t)+c_{2}sin(10t)+2/9 cos(8t)

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10y^{''}+1000y=80cos(8t)

10 y^{^{''}} + 1000 y = 80 cos (8 t)

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

Solution steps

10 y^{''} (t) + 1000 y = 80 cos (8 t)

Solve linear ODE:

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

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

\frac{d ^{3}}{d x ^{3}} (2 sin (2 x))

\int x^{3} ln (x^{4}) d x

\frac{d}{d x} (ln (\frac{x}{1 + x}))

\frac{d}{d x} (4 x e^{- 2 x} cos (4 π x + 30))

\int 6 x + \frac{1}{x ^{2}} d x

What is the solution for 10y^{''}+1000y=80cos(8t) ?
The solution for 10y^{''}+1000y=80cos(8t) is y=c_{1}cos(10t)+c_{2}sin(10t)+2/9 cos(8t)