What is the solution for y^{''}+9y=27x^3 ?

The solution for y^{''}+9y=27x^3 is y=c_{1}cos(3x)+c_{2}sin(3x)+3x^3-2x

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y^{''}+9y=27x^3

y^{^{''}} + 9 y = 27 x^{3}

y = c_{1} cos (3 x) + c_{2} sin (3 x) + 3 x^{3} - 2 x

Solution steps

y^{''} (x) + 9 y = 27 x^{3}

Solve linear ODE:

y = c_{1} cos (3 x) + c_{2} sin (3 x) + 3 x^{3} - 2 x

y = c_{1} cos (3 x) + c_{2} sin (3 x) + 3 x^{3} - 2 x

y^{^{''}} - 4 y = 3 e^{2 x}

\frac{1}{4} y^{^{''}} + 4 y = tan (4 t) - \frac{1}{2} e^{2 t}

y^{^{''''}} + 2 y^{^{''}} + y = 11 + cos (3 t)

y^{^{''}} + 4 y = sin (3 t), y (0) = 1, y^{^{'}} (0) = 0

y^{^{''}} - 2 y^{^{'}} - 3 y = 12 e x - 6

What is the solution for y^{''}+9y=27x^3 ?
The solution for y^{''}+9y=27x^3 is y=c_{1}cos(3x)+c_{2}sin(3x)+3x^3-2x