$y(x)=e^{-2x}(1+\frac{C}{x})$

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

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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$\frac{C}{x{e}^{2x}}$

Submission $2(\frac{2}{3}$ points$)$ Wednesday, February $5,202505$:$56$ PM MST

Find the general solution of the given differential equation.

$y(x)=e^{x\frac{dy}{dx}+(2x+1)y}=e^{-2x}(1+\frac{C}{x})$

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

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.$)$