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

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

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

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

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

Solution steps

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

Solve linear ODE:

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

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

f (x) = \frac{1}{4 x}

\frac{d}{d x} (x^{3} e^{3 x})

20 e^{- x}

\frac{d}{d x} (3 e^{- x} \cdot tan (3 x))

\int (\frac{ln ( x )}{x ^{3}}) d x

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