Solving y'(x) + x*y''(x) with UDC

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autobot.d
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[d]/[/dx](x*[dy]/[/dx]) = A*x

is that equivalent to saying y'(x) + x*y''(x) = A*x

then use the method of undetermined coefficients to solve it for y?

Just need a start, not the answer. Thanks.
 
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You have an exact derivative on the left side as it stands. Just immediately take an antiderivative to get started.