/sci/ - Science & Math » Thread #11488877

2KiB, 482x114, sci.png

View Same Google iqdb SauceNAO

Anonymous Sat 21 Mar 11:19:07 2020 No.11488877 View Reply Original Report

Quoted By: >>11488954 >>11489012 >>11489019

I was doing some diff eq exercises and I reached this problem. I tried y'=p(x) but with no result. And I managed to remove the square by manipulating differentials but got nowhere. So what does sci suggests?

Anonymous

Anonymous Sat 21 Mar 2020 11:57:07 No.11488954 Report

Quoted By:

>>11488877
first start by letting z=y'

Anonymous

Anonymous Sat 21 Mar 2020 12:31:07 No.11489012 Report

Quoted By: >>11489036 >>11489039

>>11488877
Let y' = p(x)
Solve the quadratic for p'(x).
substitute p(x) = x^2 - h(x)^2
Magic.

Anonymous

Anonymous Sat 21 Mar 2020 12:33:49 No.11489019 Report

Quoted By: >>11489035

>>11488877
Differentiate it with respect to x:

$y'' + x y''' - \frac{1}{2} y'' y''' - y'' = 0 \\<br />y''' \left(x - \frac{1}{2} y'' \right) = 0<br />$
Either $y''' = 0$ which gives the solution candidates $y = c x^2 - x$ or $\left( x - \frac{1}{2} y'' \right) = 0$ which gives the solution candidate $y = \frac{1}{3} x^3 - x$ .
By pluging the candidates in the original equation you see that only
$y = \pm x^2 - x$
work.

Anonymous

Anonymous Sat 21 Mar 2020 12:42:11 No.11489035 Report

Quoted By:

>>11489019
After I did other solved examples I got, alone, y=1/3*x^3-x, but in solution manual is y=-x^2-x. Thanks for help. I will use differentiation of original eq more.

Anonymous

Anonymous Sat 21 Mar 2020 12:43:36 No.11489036 Report

Quoted By:

>>11489012
This gives
(+/-)x^2 - x
without the other bullshit solution btw.

Anonymous

Anonymous Sat 21 Mar 2020 12:45:24 No.11489039 Report

Quoted By:

>>11489012
Thanks for help.

Capcode	All Only User Posts Only Moderator Posts Only Admin Posts Only Developer Posts
Show Posts	All Only With Images Only Without Images
Deleted Posts	All Only Deleted Posts Only Non-Deleted Posts
Ghost Posts	All Only Ghost Posts Only Non-Ghost Posts
Post Type	All Only Sticky Threads Only Opening Posts Only Reply Posts
Results	All Grouped By Threads
Order	Latest Posts First Oldest Posts First

Your latest searches