What is the solution for x^{''}+x=9cos(8t) ?

The solution for x^{''}+x=9cos(8t) is x=c_{1}cos(t)+c_{2}sin(t)-1/7 cos(8t)

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x^{''}+x=9cos(8t)

x^{^{''}} + x = 9 cos (8 t)

x = c_{1} cos (t) + c_{2} sin (t) - \frac{1}{7} cos (8 t)

Solution steps

x^{''} (t) + x = 9 cos (8 t)

Solve linear ODE:

x = c_{1} cos (t) + c_{2} sin (t) - \frac{1}{7} cos (8 t)

x = c_{1} cos (t) + c_{2} sin (t) - \frac{1}{7} cos (8 t)

y^{^{''}} + y = - sec (x)

(D^{2} - 1) y = e^{x}

y^{^{''}} + \frac{53}{7} \cdot y^{^{'}} + 49 x = 0

2 y^{^{''}} - 18 y^{^{'}} = 6 tan (3 x)

D (f (x)) = 4 sec (4 x) tan (4) (x)

What is the solution for x^{''}+x=9cos(8t) ?
The solution for x^{''}+x=9cos(8t) is x=c_{1}cos(t)+c_{2}sin(t)-1/7 cos(8t)