What is the solution for y^{''}+8y^'+17y=17x^2-x+28 ?

The solution for y^{''}+8y^'+17y=17x^2-x+28 is y=e^{-4x}(c_{1}cos(x)+c_{2}sin(x))+x^2-x+2

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y^{''}+8y^'+17y=17x^2-x+28

y^{^{''}} + 8 y^{^{'}} + 17 y = 17 x^{2} - x + 28

y = e^{- 4 x} (c_{1} cos (x) + c_{2} sin (x)) + x^{2} - x + 2

Solution steps

y^{''} (x) + 8 y^{'} (x) + 17 y = 17 x^{2} - x + 28

Solve linear ODE:

y = e^{- 4 x} (c_{1} cos (x) + c_{2} sin (x)) + x^{2} - x + 2

y = e^{- 4 x} (c_{1} cos (x) + c_{2} sin (x)) + x^{2} - x + 2

\frac{d ^{2} y}{d x ^{2}} + 4 \frac{d y}{d x} + 3 y = e^{- 2 x}

y^{^{''}} - 4 y^{^{'}} + 5 y = 5 t

\frac{d ^{2} y}{d x ^{2}} + y = x

y^{^{''}} - 4 y = 4 x^{2} e^{2 x}, y (0) = 0, y^{^{'}} (0) = 0

y^{^{''}} + 9 y = \frac{1}{( cos ( 3 x ) )}, y (0) = 0, y^{^{'}} (0) = 0

What is the solution for y^{''}+8y^'+17y=17x^2-x+28 ?
The solution for y^{''}+8y^'+17y=17x^2-x+28 is y=e^{-4x}(c_{1}cos(x)+c_{2}sin(x))+x^2-x+2