Question $2$

Find the general solution of the given differential equation.

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y$^\{\backslash$prime$\}+3$ x$^\{2\}$ y$=$x$^\{2\}$

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Select one of the options presented below.

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y$($x$)=$

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Give the largest interval over which the general solution is defined $($think about the implications of any singular points$).$

Select one of the options presented below.

Determine whether there are any transient terms in the general solution.

Select one of the options presented below.