Strange equation

iratus

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 ???

Thanks in advance

shawsend

MHF Hall of Honor
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.

Last edited:

iratus

So how is this equation can be solved ??? (Happy)

TheEmptySet

MHF Hall of Honor
So how is this equation can be solved ??? (Happy)

Your orginal idea will work

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.

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