What is the solution for y^{''}+9y=18x+36sin(x) ?

The solution for y^{''}+9y=18x+36sin(x) is y=c_{1}cos(3x)+c_{2}sin(3x)+2x+9/2 sin(x)

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y^{''}+9y=18x+36sin(x)

y^{^{''}} + 9 y = 18 x + 36 sin (x)

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

Solution steps

y^{''} (x) + 9 y = 18 x + 36 sin (x)

Solve linear ODE:

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

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

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

y^{^{''}} - 6 y^{^{'}} + 9 y = 10 e^{3 x}

y^{^{''}} - 4 y^{^{'}} + 4 y = \frac{e ^{- 2 x}}{1 + x ^{2}}

y^{^{''''}} + 7 y^{^{''}} + 6 = 0

y^{^{''}} - 3 y^{^{'}} + 2 y = 11 e^{3 x}

What is the solution for y^{''}+9y=18x+36sin(x) ?
The solution for y^{''}+9y=18x+36sin(x) is y=c_{1}cos(3x)+c_{2}sin(3x)+2x+9/2 sin(x)