A community for students.
Here's the question you clicked on:
 0 viewing
anonymous
 one year ago
Practice... (made up an example).
anonymous
 one year ago
Practice... (made up an example).

This Question is Closed

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0\(\large \displaystyle \int_{}^{}x~dx~=~\frac{x^2}{2}\) (of course, we omit the +c) So the integrating factor \(\large e^{\rm H(x)}\) is in this case \(\large e^{x^2/2}\). And now we multiply everything by this integrating factor. \(\large y'~e^{x^2/2}+y~e^{x^2/2}~x=3~e^{x^2/2}\) now the simple use of the product rule use (( which I found very clever as I read... very cool to come up with "integrating factor" in such equations as y' + p(x) y = q(x) )) \(\large \displaystyle \frac{d}{dx}\left[y~e^{x^2/2}\right]=3~e^{x^2/2}\) Integrating both sides \(\large \displaystyle y~e^{x^2/2}=\int 3~e^{x^2/2}~dx\) No closed form.... BUT....

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0\(\displaystyle \large e^x=\sum_{n=0}^{\infty}\frac{x^n}{n!} \) \(\displaystyle \large e^{x^2/2}=\sum_{n=0}^{\infty}\frac{x^{2n}}{2^n~n!} \) \(\displaystyle \large \int e^{x^2/2}~ dx=\int \sum_{n=0}^{\infty}\frac{x^{2n}}{2^n~n!}~dx \) \(\displaystyle \large \int e^{x^2/2}~ dx=\sum_{n=0}^{\infty}\frac{x^{2n+1}}{(2n+1)~2^n~n!} \) \(\displaystyle \large \int 3e^{x^2/2}~ dx=3\sum_{n=0}^{\infty}\frac{x^{2n+1}}{(2n+1)~2^n~n!} \)

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0\(\displaystyle \Large y=\frac{\displaystyle 3\sum_{n=0}^{\infty}\frac{x^{2n+1}}{(2n+1)~2^n~n!}+C }{~~~~~~~~~~~e^{x^2/2}~~~~~~~~~} \)

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0@radar @wio @triciaal Is this solution that I came up is super weird? Or is my example just impossible? Or did I do something totally incorrect?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0I personally don't see any errors in your work. However, I've never taken a formal diff eq course, I just learned it on my own, so not sure if there are any special conventions about this kind of stuff. Other than that, nothing wrong with the calc itself.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0I really want to say that my example is very bad, because I can't get an elementary function when I integrate e^(x^2/2), that is why y'+yx=3. If I had a teacher.... but I read just a couple hours ago in my calculus book.... tnx for checking, will see what others say if they see this.
Ask your own question
Sign UpFind more explanations on OpenStudy
Your question is ready. Sign up for free to start getting answers.
spraguer
(Moderator)
5
→ View Detailed Profile
is replying to Can someone tell me what button the professor is hitting...
23
 Teamwork 19 Teammate
 Problem Solving 19 Hero
 Engagement 19 Mad Hatter
 You have blocked this person.
 ✔ You're a fan Checking fan status...
Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.