What is the solution for y^{''}-2y^'-3y=64xe^{-x} ?

The solution for y^{''}-2y^'-3y=64xe^{-x} is y=c_{1}e^{3x}+c_{2}e^{-x}-8x^2e^{-x}-4e^{-x}x

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y^{''}-2y^'-3y=64xe^{-x}

y^{^{''}} - 2 y^{^{'}} - 3 y = 64 x e^{- x}

y = c_{1} e^{3 x} + c_{2} e^{- x} - 8 x^{2} e^{- x} - 4 e^{- x} x

Solution steps

y^{''} (x) - 2 y^{'} (x) - 3 y = 64 x e^{- x}

Solve linear ODE:

y = c_{1} e^{3 x} + c_{2} e^{- x} - 8 x^{2} e^{- x} - 4 e^{- x} x

y = c_{1} e^{3 x} + c_{2} e^{- x} - 8 x^{2} e^{- x} - 4 e^{- x} x

\int_{0}^{a} (\frac{m}{2 π ( a - x )})^{5} d x

y = 3 x^{4} - 3 x^{2}, y = 3 x^{2}

x \to 2 lim (\frac{2 x + 4}{x - 7})

\int_{0}^{\infty} e^{- 0.2 x} d x

\int 1 0^{- 3 x} d x

What is the solution for y^{''}-2y^'-3y=64xe^{-x} ?
The solution for y^{''}-2y^'-3y=64xe^{-x} is y=c_{1}e^{3x}+c_{2}e^{-x}-8x^2e^{-x}-4e^{-x}x