What is the solution for y^{''}+11y^'+28y=-2e^{2x}+1 ?

The solution for y^{''}+11y^'+28y=-2e^{2x}+1 is y=c_{1}e^{-4x}+c_{2}e^{-7x}-1/27 e^{2x}+1/28

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y^{''}+11y^'+28y=-2e^{2x}+1

y^{^{''}} + 11 y^{^{'}} + 28 y = - 2 e^{2 x} + 1

y = c_{1} e^{- 4 x} + c_{2} e^{- 7 x} - \frac{1}{27} e^{2 x} + \frac{1}{28}

Solution steps

y^{''} (x) + 11 y^{'} (x) + 28 y = - 2 e^{2 x} + 1

Solve linear ODE:

y = c_{1} e^{- 4 x} + c_{2} e^{- 7 x} - \frac{1}{27} e^{2 x} + \frac{1}{28}

y = c_{1} e^{- 4 x} + c_{2} e^{- 7 x} - \frac{1}{27} e^{2 x} + \frac{1}{28}

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

4 y^{^{''}} + 9 y = 15

y^{^{''}} - 3 y^{^{'}} + 2 y = sin (x), y (0) = 0, y^{^{'}} (0) = 2

y^{^{''}} + y = sec^{3} (x)

y^{^{''}} + 4 y^{^{'}} + 3 y = 9 e^{- 3 x}

What is the solution for y^{''}+11y^'+28y=-2e^{2x}+1 ?
The solution for y^{''}+11y^'+28y=-2e^{2x}+1 is y=c_{1}e^{-4x}+c_{2}e^{-7x}-1/27 e^{2x}+1/28