What is the solution for y^{''}+y^'-6y=2x^2+1 ?

The solution for y^{''}+y^'-6y=2x^2+1 is y=c_{1}e^{2x}+c_{2}e^{-3x}-(x^2)/3-x/9-8/27

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y^{''}+y^'-6y=2x^2+1

y^{^{''}} + y^{^{'}} - 6 y = 2 x^{2} + 1

y = c_{1} e^{2 x} + c_{2} e^{- 3 x} - \frac{x ^{2}}{3} - \frac{x}{9} - \frac{8}{27}

Solution steps

y^{''} (x) + y^{'} (x) - 6 y = 2 x^{2} + 1

Solve linear ODE:

y = c_{1} e^{2 x} + c_{2} e^{- 3 x} - \frac{x ^{2}}{3} - \frac{x}{9} - \frac{8}{27}

y = c_{1} e^{2 x} + c_{2} e^{- 3 x} - \frac{x ^{2}}{3} - \frac{x}{9} - \frac{8}{27}

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

y^{^{''}} + 9 y = cos (x) + \frac{1}{3} cos (3 x)

y^{^{''}} - 4 y^{^{'}} + 5 y = e^{2 x} sec^{3} (x)

y^{^{''}} - 9 y = (x^{2} - 4) sin (3 x)

y^{^{''}} + 8 y^{^{'}} = 64 x

What is the solution for y^{''}+y^'-6y=2x^2+1 ?
The solution for y^{''}+y^'-6y=2x^2+1 is y=c_{1}e^{2x}+c_{2}e^{-3x}-(x^2)/3-x/9-8/27