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

[Jeff12341234]

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

 

[rock.freak667]

For y=ux³e^x 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= ux³e^x
y= UV where U=u and V=x³e^x

dU/dx = u'

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

So recalculate what y' and y'' would be.

 

[Jeff12341234]

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?

 

[rock.freak667]

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=ux³e^x to get y' = ue^xx²(x+3) ?

 

[Jeff12341234]

I just used my Ti-nSpire CAS and Wolfram alpha http://www.wolframalpha.com/widgets/gallery/view.jsp?id=96055f5b06bf9381ac43879351642cf5

 

[rock.freak667]

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.

 

[Jeff12341234]

How would you type that in there?

 

[Jeff12341234]

I got it. you just type u(x) instead of u

 

[rock.freak667]

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.