D.E. Reduction of Order: Stuck on step 2

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Homework Help Overview

The discussion revolves around the differentiation of a function involving a product of a variable and an exponential term, specifically in the context of reduction of order for differential equations. Participants are exploring the correct application of differentiation rules, particularly the product rule, and the implications of treating certain variables as constants versus functions of x.

Discussion Character

  • Conceptual clarification, Mathematical reasoning, Assumption checking

Approaches and Questions Raised

  • Participants are attempting to differentiate the function y=ux3ex and are questioning the validity of their methods. There is a focus on understanding why certain approaches may lead to incorrect results, particularly regarding the treatment of u as a constant versus a function of x.

Discussion Status

Some participants have acknowledged the necessity of using the product rule for differentiation and are seeking clarification on their initial attempts. There is an ongoing exploration of the reasoning behind the differentiation process, with no explicit consensus reached yet.

Contextual Notes

Participants are discussing the implications of assuming u is a constant when it is actually a function of x, which affects the differentiation process. There is also mention of using computational tools to assist with differentiation, though the effectiveness of these tools in this context is questioned.

Jeff12341234
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When you do the 1st and 2nd derivatives of y2, you're supposed to get u' and u'' in your answer. My question is why can't you do it the way I've started to do it? Or, why are my answers for y2' and y2'' wrong?

http://i.imgur.com/OarDiuW.jpg
 
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For y=ux3ex you need to apply the product rule to get y' and again with y''.

You will inevitably get terms with u' and u'' since

for y= ux3ex
y= UV where U=u and V=x3ex

dU/dx = u'

and dy/dx = V(dU/dx)+U(dV/dx)

So recalculate what y' and y'' would be.
 
Yea, i see that I'm supposed to use the product rule. I want to know *why* I can't do it the way I'm doing it. I mean, my answers aren't wrong so why can't I use them?
 
Jeff12341234 said:
Yea, i see that I'm supposed to use the product rule. I want to know *why* I can't do it the way I'm doing it. I mean, my answers aren't wrong so why can't I use them?

Can you please show how you differentiated y=ux3ex to get y' = uexx2(x+3) ?
 
Jeff12341234 said:
I just used my Ti-nSpire CAS and Wolfram alpha

I asked because your differentiation to get y' went under the assumption that u was a constant. When it is in fact a function of x. So you will need to recalculate it with u being a function of x.
 
How would you type that in there?
 
I got it. you just type u(x) instead of u
 
Jeff12341234 said:
How would you type that in there?

It might be more beneficial for you to do it by hand. I am not sure how you would do it in your calculator though.
 

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