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

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