Consider the following differential equation.

$(x1)\frac{dy}{dx}(x2)y=4x{e}^{-x}$

Find the coefficient function $f(x)$ when the given differential equation is written in the standard form $\frac{dy}{dx}f(x)y=f(x).$

$f(x)=$

Find the integrating factor for the differential equation.

Stride

Find the general solution of the given differential equation.

mas

Give the largest interval $z$ over which the general solution is defined. $[$Think about the implications of any singular points. Enter your answer using interval notation.$]$

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Determine whether there are any transient terms in the general solution. $($Enter the transient terms as a comma$-$separated list; if there are none, enter None.$)$

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