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

1. Feb 24, 2013

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

Last edited by a moderator: Feb 24, 2013
2. Feb 24, 2013

rock.freak667

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.

3. Feb 24, 2013

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?

4. Feb 24, 2013

rock.freak667

Can you please show how you differentiated y=ux3ex to get y' = uexx2(x+3) ?

5. Feb 24, 2013

Jeff12341234

6. Feb 24, 2013

rock.freak667

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.

7. Feb 24, 2013

Jeff12341234

How would you type that in there?

8. Feb 24, 2013

Jeff12341234

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

9. Feb 24, 2013

rock.freak667

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.