D.E.: Reduction of Order: Non-shortcut method question

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Jeff12341234
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I don't know what to do with the x^3*e^x on the left side of the page. In the example the instructor gave for a different problem, you couldn't solve for x. In this problem you can so what does that mean I need to do with it?

Handwritten notes on lined paper solving a reduction of order problem: substituting y2 = u x^3 e^x, deriving y2'' and simplifying to u'' x^3 e^x + 4u' x^3 e^x = 0, then solving u' = x^-4 and giving y2 = x^3 e^x times the integral of x^-4 dx, ending with the general solution c1 x^3 e^x + c2 e^x.
 

Discussion

So do you always just ignore the factor that doesn't contain the u(x) function like I just did in this example?
 

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