What is the solution for y^{''}-9y=20sin(x)+3x^2 ?

The solution for y^{''}-9y=20sin(x)+3x^2 is y=c_{1}e^{3x}+c_{2}e^{-3x}-2sin(x)-(x^2)/3-2/27

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y^{''}-9y=20sin(x)+3x^2

y^{^{''}} - 9 y = 20 sin (x) + 3 x^{2}

y = c_{1} e^{3 x} + c_{2} e^{- 3 x} - 2 sin (x) - \frac{x ^{2}}{3} - \frac{2}{27}

Solution steps

y^{''} (x) - 9 y = 20 sin (x) + 3 x^{2}

Solve linear ODE:

y = c_{1} e^{3 x} + c_{2} e^{- 3 x} - 2 sin (x) - \frac{x ^{2}}{3} - \frac{2}{27}

y = c_{1} e^{3 x} + c_{2} e^{- 3 x} - 2 sin (x) - \frac{x ^{2}}{3} - \frac{2}{27}

y^{^{''}} + y^{^{'}} + y = k x

y^{^{''}} - y^{^{'}} - 2 y = 2 x^{3} - 3 x^{2} + 8 x + 1

y^{^{''}} + 16 y = 8 e^{3 x}

y^{^{''}} + 4 y = x - \frac{x ^{2}}{20}

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

What is the solution for y^{''}-9y=20sin(x)+3x^2 ?
The solution for y^{''}-9y=20sin(x)+3x^2 is y=c_{1}e^{3x}+c_{2}e^{-3x}-2sin(x)-(x^2)/3-2/27