What is the solution for y^{''}+5y^'+4y=8x^2+6e^{-x} ?

The solution for y^{''}+5y^'+4y=8x^2+6e^{-x} is y=c_{1}e^{-x}+c_{2}e^{-4x}+2x^2-5x+21/4+2xe^{-x}

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y^{''}+5y^'+4y=8x^2+6e^{-x}

y^{^{''}} + 5 y^{^{'}} + 4 y = 8 x^{2} + 6 e^{- x}

y = c_{1} e^{- x} + c_{2} e^{- 4 x} + 2 x^{2} - 5 x + \frac{21}{4} + 2 x e^{- x}

Solution steps

y^{''} (x) + 5 y^{'} (x) + 4 y = 8 x^{2} + 6 e^{- x}

Solve linear ODE:

y = c_{1} e^{- x} + c_{2} e^{- 4 x} + 2 x^{2} - 5 x + \frac{21}{4} + 2 x e^{- x}

y = c_{1} e^{- x} + c_{2} e^{- 4 x} + 2 x^{2} - 5 x + \frac{21}{4} + 2 x e^{- x}

\int x sin (\frac{1}{10} x) d x

\int x + 1 ln (x + 1) d x

\int 5 x (2 + 3 x^{2})^{8} d x

\frac{10}{s ^{3} + s ^{2} + 10 s}

\frac{d}{d x} ((x^{2} + 1)^{2 x - x^{2}})

What is the solution for y^{''}+5y^'+4y=8x^2+6e^{-x} ?
The solution for y^{''}+5y^'+4y=8x^2+6e^{-x} is y=c_{1}e^{-x}+c_{2}e^{-4x}+2x^2-5x+21/4+2xe^{-x}