A community for students.
Here's the question you clicked on:
 0 viewing
 2 years ago
Find two power series solutions of the given differential equation about the ordinary point x=0: y''xy=0
 2 years ago
Find two power series solutions of the given differential equation about the ordinary point x=0: y''xy=0

This Question is Closed

Outkast3r09
 2 years ago
Best ResponseYou've already chosen the best response.1\[y=\sum_{n=0}^\infty c_nx^n\]

Outkast3r09
 2 years ago
Best ResponseYou've already chosen the best response.1\[y'=\sum_{n=1}^\infty c_nnx^{n1}\]

Outkast3r09
 2 years ago
Best ResponseYou've already chosen the best response.1\[y''=\sum_{n=2}^\infty c_n(n)(n1)x^{n2}\]

TuringTest
 2 years ago
Best ResponseYou've already chosen the best response.0oh I need a review on this bookmark*

Outkast3r09
 2 years ago
Best ResponseYou've already chosen the best response.1i'm pretty sure i have it down so you can come check it after \[y''xy=\sum_{n=2}^\infty c_nn(n1)x^{n2}x\sum_{n=0}^\infty c_nx^n\]

Outkast3r09
 2 years ago
Best ResponseYou've already chosen the best response.1\[\sum_{n=2}^\infty c_nn(n1)x^{n2}\sum_{n=0}^\infty c_nx^{n+1}\]

Outkast3r09
 2 years ago
Best ResponseYou've already chosen the best response.1\[k=n2\] \[k+2=n\] \[\sum_{k=0}^\infty c_{k+2}(k+2)(k+21)x^k\sum_{n=0}^\infty c_nx^{n+1}=0\]

Outkast3r09
 2 years ago
Best ResponseYou've already chosen the best response.1\[\sum_{k=0}^\infty c_{k+2}(k+2)(k+1)x^k\sum_{k=1}^\infty c_{k1}x^k\] where \[k=n+1\] \[k1=n\]

Outkast3r09
 2 years ago
Best ResponseYou've already chosen the best response.1pull out one term k=0 of first \[2c_2+\sum_{k=1}^\infty c_{k+2}(k+2)(k+1)x^k\sum_{k=1}^\infty c_{k1}x^k\]

Outkast3r09
 2 years ago
Best ResponseYou've already chosen the best response.1\[2c_2+\sum_{k=1}^\infty [c_{k+2}(k+2)(k+1)c_{k1}]x^k\]

Outkast3r09
 2 years ago
Best ResponseYou've already chosen the best response.1since identity 0=0 the sum and \[2c_2=0\] \[c_2=0\]

Outkast3r09
 2 years ago
Best ResponseYou've already chosen the best response.1\[c_{k+2}(k+2)(k+1)=c_{k1}\] \[c_{k+2}=\frac{c_{k1}}{(k+2)(k+1)}\]

Outkast3r09
 2 years ago
Best ResponseYou've already chosen the best response.1for k=1,2,3,4,5,6......

Outkast3r09
 2 years ago
Best ResponseYou've already chosen the best response.1k=1 \[c_3=\frac{c_0}{3*2}\] k=2 \[c_4=\frac{c_1}{4*3}\] for k =3 \[c_5=\frac{c_2}{constant}\] =\[c_2=0\] k=4 \[c_6=\frac{c_3}{6*5)}=\frac{c_0}{6*5*3*2}\]

Outkast3r09
 2 years ago
Best ResponseYou've already chosen the best response.1k=5 \[c_7=\frac{c_4}{7*6}=\frac{c_1}{7*6*4*3}\]

Outkast3r09
 2 years ago
Best ResponseYou've already chosen the best response.1@TuringTest look correct so far?

TuringTest
 2 years ago
Best ResponseYou've already chosen the best response.0like I said: *bookmark I want you to remind me; it's been a while... maybe @experimentX can verify better than me

experimentX
 2 years ago
Best ResponseYou've already chosen the best response.0jeez ... i forgot all those stuffs. i need to review it myself.

TuringTest
 2 years ago
Best ResponseYou've already chosen the best response.0hm... @Zarkon care to verify a DE series solution?

Outkast3r09
 2 years ago
Best ResponseYou've already chosen the best response.1Is zarkon the computer on lol

experimentX
 2 years ago
Best ResponseYou've already chosen the best response.0these standard equations power solutions look intimidating ...

Outkast3r09
 2 years ago
Best ResponseYou've already chosen the best response.1\[y=c_0+c_1x+0+\frac{c_0}{3*2}x^3+\frac{c_1}{4*3}x^4+0+\frac{c_0}{2*3*5*6}x^6\] \[+\frac{c_1}{3*4*6*7}x^7+0......\]

Outkast3r09
 2 years ago
Best ResponseYou've already chosen the best response.1\[y_1(x)=1+\frac{1}{2*3}x^3+\frac{1}{2*3*5*6}x^6...\] \[y_2(x)=x+\frac{1}{3*4}x^4+\frac{1}{3*4*6*7}x^7.......\]

experimentX
 2 years ago
Best ResponseYou've already chosen the best response.0what kind of function is this http://www.wolframalpha.com/input/?i=y%27%27++xy%3D0

experimentX
 2 years ago
Best ResponseYou've already chosen the best response.0Using Maple I found this solution \[ C0+C1*x+(1/6)*C0*x^3+(1/12)*C1*x^4+\\ (1/180)*C0*x^6+(1/504)*C1*x^7+O(x^8) \]

Outkast3r09
 2 years ago
Best ResponseYou've already chosen the best response.1only i left it not multiplied so i can creat a summation

experimentX
 2 years ago
Best ResponseYou've already chosen the best response.0well, i guess you are right ... i never liked power series solution you know!!
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.