What is the solution for (D^2+9)y=81x^2+(14cos(x)) ?

The solution for (D^2+9)y=81x^2+(14cos(x)) is y=c_{1}cos(3x)+c_{2}sin(3x)+9x^2-2+7/4 cos(x)

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(D^2+9)y=81x^2+(14cos(x))

(D^{2} + 9) y = 81 x^{2} + (14 cos (x))

y = c_{1} cos (3 x) + c_{2} sin (3 x) + 9 x^{2} - 2 + \frac{7}{4} cos (x)

Solution steps

(D^{2} + 9) y = 81 x^{2} + 14 cos (x)

Solve linear ODE:

y = c_{1} cos (3 x) + c_{2} sin (3 x) + 9 x^{2} - 2 + \frac{7}{4} cos (x)

y = c_{1} cos (3 x) + c_{2} sin (3 x) + 9 x^{2} - 2 + \frac{7}{4} cos (x)

y^{^{'''}} - 6 y^{^{''}} + 12 y^{^{'}} - 8 y = t^{- 2} e^{2 t}

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

y^{^{''}} - y = x - 1

y^{^{''}} + 4 y = t^{2} + 8 e^{t}, y (0) = 0, y^{^{'}} (0) = 7

x^{^{''}} + 10 x^{^{'}} + 16 x = 10 sin (4 t)

What is the solution for (D^2+9)y=81x^2+(14cos(x)) ?
The solution for (D^2+9)y=81x^2+(14cos(x)) is y=c_{1}cos(3x)+c_{2}sin(3x)+9x^2-2+7/4 cos(x)