What is the solution for x^{''}+49x=52cos(6t) ?

The solution for x^{''}+49x=52cos(6t) is x=c_{1}cos(7t)+c_{2}sin(7t)+4cos(6t)

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x^{''}+49x=52cos(6t)

x^{^{''}} + 49 x = 52 cos (6 t)

x = c_{1} cos (7 t) + c_{2} sin (7 t) + 4 cos (6 t)

Solution steps

x^{''} (t) + 49 x = 52 cos (6 t)

Solve linear ODE:

x = c_{1} cos (7 t) + c_{2} sin (7 t) + 4 cos (6 t)

x = c_{1} cos (7 t) + c_{2} sin (7 t) + 4 cos (6 t)

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

y^{^{''}} - 5 y^{^{'}} + 6 y = 12 x - 4

y^{^{''}} - y = 4 e - x^{1} - e - 2 x

y^{^{''}} - 2 y^{^{'}} - 3 y = 12 e^{3 x}

y^{^{''}} + 2 y^{^{'}} + 2 y = e^{x} cos (x)

What is the solution for x^{''}+49x=52cos(6t) ?
The solution for x^{''}+49x=52cos(6t) is x=c_{1}cos(7t)+c_{2}sin(7t)+4cos(6t)