What is the solution for y^{''}+8y^'+7y=-8-x+24x^2+7x^3 ?

The solution for y^{''}+8y^'+7y=-8-x+24x^2+7x^3 is y=c_{1}e^{-x}+c_{2}e^{-7x}+x^3-x

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y^{''}+8y^'+7y=-8-x+24x^2+7x^3

y^{^{''}} + 8 y^{^{'}} + 7 y = - 8 - x + 24 x^{2} + 7 x^{3}

y = c_{1} e^{- x} + c_{2} e^{- 7 x} + x^{3} - x

Solution steps

y^{''} (x) + 8 y^{'} (x) + 7 y = - 8 - x + 24 x^{2} + 7 x^{3}

Solve linear ODE:

y = c_{1} e^{- x} + c_{2} e^{- 7 x} + x^{3} - x

y = c_{1} e^{- x} + c_{2} e^{- 7 x} + x^{3} - x

\int x^{2} \cdot 1 - x^{2} d x

y^{^{''}} + 121 y = cos (6 t)

\int \frac{3 ^{x}}{x} d x

3 y^{^{''}} + 8 y^{^{'}} - 3 y = 0

\int (1 + cos^{2} (x)) d x

What is the solution for y^{''}+8y^'+7y=-8-x+24x^2+7x^3 ?
The solution for y^{''}+8y^'+7y=-8-x+24x^2+7x^3 is y=c_{1}e^{-x}+c_{2}e^{-7x}+x^3-x