What is the solution for y^{''}-2y^'+37y=e^xcos(6x) ?

The solution for y^{''}-2y^'+37y=e^xcos(6x) is y=e^x(c_{1}cos(6x)+c_{2}sin(6x))+(e^xxsin(6x))/(12)

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y^{''}-2y^'+37y=e^xcos(6x)

y^{^{''}} - 2 y^{^{'}} + 37 y = e^{x} cos (6 x)

y = e^{x} (c_{1} cos (6 x) + c_{2} sin (6 x)) + \frac{e ^{x} x sin ( 6 x )}{12}

Solution steps

y^{''} (x) - 2 y^{'} (x) + 37 y = e^{x} cos (6 x)

Solve linear ODE:

y = e^{x} (c_{1} cos (6 x) + c_{2} sin (6 x)) + \frac{e ^{x} x sin ( 6 x )}{12}

y = e^{x} (c_{1} cos (6 x) + c_{2} sin (6 x)) + \frac{e ^{x} x sin ( 6 x )}{12}

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

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

y^{^{''}} - y = 8

y^{^{''}} + y = H (t) - 2 H (t - \frac{b}{2}) + H (t - b)

y^{^{''}} + 3 y^{^{'}} - 4 y = 2

What is the solution for y^{''}-2y^'+37y=e^xcos(6x) ?
The solution for y^{''}-2y^'+37y=e^xcos(6x) is y=e^x(c_{1}cos(6x)+c_{2}sin(6x))+(e^xxsin(6x))/(12)