What is the solution for y^{''}-9y=4-30x^2+9x^4 ?

The solution for y^{''}-9y=4-30x^2+9x^4 is y=c_{1}e^{3x}+c_{2}e^{-3x}-x^4+2x^2

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y^{''}-9y=4-30x^2+9x^4

y^{^{''}} - 9 y = 4 - 30 x^{2} + 9 x^{4}

y = c_{1} e^{3 x} + c_{2} e^{- 3 x} - x^{4} + 2 x^{2}

Solution steps

y^{''} (x) - 9 y = 4 - 30 x^{2} + 9 x^{4}

Solve linear ODE:

y = c_{1} e^{3 x} + c_{2} e^{- 3 x} - x^{4} + 2 x^{2}

y = c_{1} e^{3 x} + c_{2} e^{- 3 x} - x^{4} + 2 x^{2}

\frac{d ^{2} y}{d x ^{2}} + y = sec^{2} (x)

y^{^{''}} + 6 y^{^{'}} + 9 y = e^{- x} cos (2 x)

\frac{d ^{2} y}{d x ^{2}} - 4 \frac{d y}{d x} + 13 y = 5 cos (2 x)

y^{^{'''}} - 6 y^{^{''}} + 11 y^{^{'}} - 6 y = - 1

4 y^{^{''}} + k y = 8 sin (t)

What is the solution for y^{''}-9y=4-30x^2+9x^4 ?
The solution for y^{''}-9y=4-30x^2+9x^4 is y=c_{1}e^{3x}+c_{2}e^{-3x}-x^4+2x^2