What is the solution for y^{''}-2y^'+82y=e^xcos(9x) ?

The solution for y^{''}-2y^'+82y=e^xcos(9x) is y=e^x(c_{1}cos(9x)+c_{2}sin(9x))+(e^xxsin(9x))/(18)

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y^{''}-2y^'+82y=e^xcos(9x)

y^{^{''}} - 2 y^{^{'}} + 82 y = e^{x} cos (9 x)

y = e^{x} (c_{1} cos (9 x) + c_{2} sin (9 x)) + \frac{e ^{x} x sin ( 9 x )}{18}

Solution steps

y^{''} (x) - 2 y^{'} (x) + 82 y = e^{x} cos (9 x)

Solve linear ODE:

y = e^{x} (c_{1} cos (9 x) + c_{2} sin (9 x)) + \frac{e ^{x} x sin ( 9 x )}{18}

y = e^{x} (c_{1} cos (9 x) + c_{2} sin (9 x)) + \frac{e ^{x} x sin ( 9 x )}{18}

y^{^{''}} - 2 y^{^{'}} - 3 y = 5 e^{4 x}, y (0) = 1, y^{^{'}} (0) = 0

y^{^{''}} - 2 y^{^{'}} - 3 y = 6

y^{^{''}} - y = 2, y (0) = 2, y^{^{'}} (0) = 0

y^{^{''}} - 2 y^{^{'}} + 5 y = sin (x)

y^{^{''}} + 4 y = 4 sec^{2} (2 t)

What is the solution for y^{''}-2y^'+82y=e^xcos(9x) ?
The solution for y^{''}-2y^'+82y=e^xcos(9x) is y=e^x(c_{1}cos(9x)+c_{2}sin(9x))+(e^xxsin(9x))/(18)