What is the solution for x^{''}+x=8cos(5t) ?

The solution for x^{''}+x=8cos(5t) is x=c_{1}cos(t)+c_{2}sin(t)-1/3 cos(5t)

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x^{''}+x=8cos(5t)

x^{^{''}} + x = 8 cos (5 t)

x = c_{1} cos (t) + c_{2} sin (t) - \frac{1}{3} cos (5 t)

Solution steps

x^{''} (t) + x = 8 cos (5 t)

Solve linear ODE:

x = c_{1} cos (t) + c_{2} sin (t) - \frac{1}{3} cos (5 t)

x = c_{1} cos (t) + c_{2} sin (t) - \frac{1}{3} cos (5 t)

y^{^{''}} + 2 y^{^{'}} + 1 = 4 sin (2 x)

1.6 q^{^{''}} + 1200 q^{^{'}} + \frac{1}{0.00001} q = 14

y^{^{'''}} + y^{^{'}} = 2

y^{^{''}} - 4 y^{^{'}} + 4 y = - 7 x + 4 x

\frac{d ^{2} y}{d x ^{2}} + a \frac{d y}{d x} = g

What is the solution for x^{''}+x=8cos(5t) ?
The solution for x^{''}+x=8cos(5t) is x=c_{1}cos(t)+c_{2}sin(t)-1/3 cos(5t)