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

[Jeff12341234]

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?

 

[Jeff12341234]

Is this answer correct?

 

[MednataMiza]

Yes, it is :)

 

[Jeff12341234]

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