What is the solution for x^{''}+x=8cos(6t) ?

The solution for x^{''}+x=8cos(6t) is x=c_{1}cos(t)+c_{2}sin(t)-8/35 cos(6t)

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x^{''}+x=8cos(6t)

x^{^{''}} + x = 8 cos (6 t)

x = c_{1} cos (t) + c_{2} sin (t) - \frac{8}{35} cos (6 t)

Solution steps

x^{''} (t) + x = 8 cos (6 t)

Solve linear ODE:

x = c_{1} cos (t) + c_{2} sin (t) - \frac{8}{35} cos (6 t)

x = c_{1} cos (t) + c_{2} sin (t) - \frac{8}{35} cos (6 t)

y^{^{''}} + 2 y^{^{'}} - 3 y = x^{2} - 1

\frac{d ^{2} x}{d t ^{2}} + 16 x = 12 cos (9 t)

y^{^{''}} - 3 y^{^{'}} - 18 y = x e^{3 x}

y^{^{''}} + y = e^{- t} sin (e^{- t}) + cos (e^{- t})

y^{^{''}} + y = \frac{x}{∣ x ∣}

What is the solution for x^{''}+x=8cos(6t) ?
The solution for x^{''}+x=8cos(6t) is x=c_{1}cos(t)+c_{2}sin(t)-8/35 cos(6t)