What is the solution for x^{''}+49x=39cos(6t) ?

The solution for x^{''}+49x=39cos(6t) is x=c_{1}cos(7t)+c_{2}sin(7t)+3cos(6t)

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x^{''}+49x=39cos(6t)

x^{^{''}} + 49 x = 39 cos (6 t)

x = c_{1} cos (7 t) + c_{2} sin (7 t) + 3 cos (6 t)

Solution steps

x^{''} (t) + 49 x = 39 cos (6 t)

Solve linear ODE:

x = c_{1} cos (7 t) + c_{2} sin (7 t) + 3 cos (6 t)

x = c_{1} cos (7 t) + c_{2} sin (7 t) + 3 cos (6 t)

4 y^{^{''}} - 8 y^{^{'}} + 4 y = e^{x} (3 x + 2) + 2 cos (x)

y^{^{''}} + 25 y = 3 sin (5 x)

y^{^{''}} + 4 y = 9 t, y (0) = 0, y (0) = 7

y^{^{''}} + 16 y = 4 x, y (0) = 1, y^{^{'}} (0) = 4

y^{^{''}} + 5 y^{^{'}} = 15 x^{2}

What is the solution for x^{''}+49x=39cos(6t) ?
The solution for x^{''}+49x=39cos(6t) is x=c_{1}cos(7t)+c_{2}sin(7t)+3cos(6t)