What is the solution for 10y^{''}+1000y=140cos(8t) ?

The solution for 10y^{''}+1000y=140cos(8t) is y=c_{1}cos(10t)+c_{2}sin(10t)+7/18 cos(8t)

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10y^{''}+1000y=140cos(8t)

10 y^{^{''}} + 1000 y = 140 cos (8 t)

y = c_{1} cos (10 t) + c_{2} sin (10 t) + \frac{7}{18} cos (8 t)

Solution steps

10 y^{''} (t) + 1000 y = 140 cos (8 t)

Solve linear ODE:

y = c_{1} cos (10 t) + c_{2} sin (10 t) + \frac{7}{18} cos (8 t)

y = c_{1} cos (10 t) + c_{2} sin (10 t) + \frac{7}{18} cos (8 t)

\int e^{2 x + 3} d x

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

\int \frac{sin ( 6 e ^{- 2 x} )}{e ^{2 x}} d x

\int_{1}^{9} \frac{1}{8 - x} d x

What is the solution for 10y^{''}+1000y=140cos(8t) ?
The solution for 10y^{''}+1000y=140cos(8t) is y=c_{1}cos(10t)+c_{2}sin(10t)+7/18 cos(8t)