What is the solution for y^{'''}-6y^{''}=cos(4x) ?

The solution for y^{'''}-6y^{''}=cos(4x) is y=c_{1}e^{6x}+c_{2}+c_{3}x-1/208 sin(4x)+3/416 cos(4x)

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y^{'''}-6y^{''}=cos(4x)

y^{^{'''}} - 6 y^{^{''}} = cos (4 x)

y = c_{1} e^{6 x} + c_{2} + c_{3} x - \frac{1}{208} sin (4 x) + \frac{3}{416} cos (4 x)

Solution steps

y^{'''} (x) - 6 y^{''} (x) = cos (4 x)

Solve linear ODE:

y = c_{1} e^{6 x} + c_{2} + c_{3} x - \frac{1}{208} sin (4 x) + \frac{3}{416} cos (4 x)

y = c_{1} e^{6 x} + c_{2} + c_{3} x - \frac{1}{208} sin (4 x) + \frac{3}{416} cos (4 x)

y^{^{''}} - 2 y^{^{'}} - 8 y = - 8 t - 18, y (0) = 1, y^{^{'}} (0) = 28

y^{^{''}} - 2 y^{^{'}} + y = e^{x} sec^{2} (x) tan (x)

y^{^{''}} - y = 2 t^{2} - t + 3 e^{- 3 t}

q^{^{''}} + 0.1 q^{^{'}} + q = v sin (0.5 t), q (0) = 0

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

What is the solution for y^{'''}-6y^{''}=cos(4x) ?
The solution for y^{'''}-6y^{''}=cos(4x) is y=c_{1}e^{6x}+c_{2}+c_{3}x-1/208 sin(4x)+3/416 cos(4x)