What is the solution for y^{'''}-5y^'+6y^'=9+5sin(x) ?

The solution for y^{'''}-5y^'+6y^'=9+5sin(x) is y=c_{1}+c_{2}cos(x)+c_{3}sin(x)+9x-(5xsin(x))/2

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y^{'''}-5y^'+6y^'=9+5sin(x)

y^{^{'''}} - 5 y^{^{'}} + 6 y^{^{'}} = 9 + 5 sin (x)

y = c_{1} + c_{2} cos (x) + c_{3} sin (x) + 9 x - \frac{5 x sin ( x )}{2}

Solution steps

y^{'''} (x) - 5 y^{'} (x) + 6 y^{'} (x) = 9 + 5 sin (x)

Solve linear ODE:

y = c_{1} + c_{2} cos (x) + c_{3} sin (x) + 9 x - \frac{5 x sin ( x )}{2}

y = c_{1} + c_{2} cos (x) + c_{3} sin (x) + 9 x - \frac{5 x sin ( x )}{2}

(d + 2) (d - 1)^{2} y = e^{- 2} x + 2 sinh (x)

y^{^{''}} + 13 y^{^{'}} + 42 y = 7 cos (4 t)

\frac{1}{2} y^{^{''}} + 2 y = 2 tan (2 t) - \frac{1}{2} e^{2 t}

y^{^{'''}} - 4 y^{^{''}} + 5 y^{^{'}} - 2 y = 2 e^{- x} + cos (x)

y^{^{''''}} + 2 y^{^{''}} + 2 = 0

What is the solution for y^{'''}-5y^'+6y^'=9+5sin(x) ?
The solution for y^{'''}-5y^'+6y^'=9+5sin(x) is y=c_{1}+c_{2}cos(x)+c_{3}sin(x)+9x-(5xsin(x))/2