# Strange equation

• May 24th 2010, 07:14 AM
iratus
Strange equation
Hello

I am new to this forum. I think that you are doing a very good job here helping people solve their problems !!!!

In few days i have one of my final course exam (I will graduate) and i have some questions that concerns me

One of them is this :

$\displaystyle y'''' * y'''= 1$

I had an idea to put y'''=u , y''''=u' but it didn't worked

How can i solve this ???

• May 24th 2010, 09:51 AM
shawsend
That's the same as vdv=dx isn't it? I mean isn't y'''' the derivative of y'''?
Same dif if is was yy'=1 or y'y'' and so forth.
• May 24th 2010, 03:33 PM
iratus
So how is this equation can be solved ??? (Happy)
• May 24th 2010, 03:52 PM
TheEmptySet
Quote:

Originally Posted by iratus
So how is this equation can be solved ??? (Happy)

let $\displaystyle u=y''' \implies u'=y^{(4)}$ this gives the equation
$\displaystyle \frac{du}{dx}u=1 \iff udu=dx \iff u^2=2x+C \iff u=\sqrt{2x+C}$
Now $\displaystyle u=y'''$ is just integrate the above three times to recover the function y.