Got Homework?
Connect with other students for help. It's a free community.
Here's the question you clicked on:
 0 viewing
Find two power series solutions of the given differential equation about the ordinary point x=0: y''xy=0
 one year ago
 one year ago
Find two power series solutions of the given differential equation about the ordinary point x=0: y''xy=0
 one year ago
 one year ago

This Question is Closed

Outkast3r09Best ResponseYou've already chosen the best response.1
\[y=\sum_{n=0}^\infty c_nx^n\]
 one year ago

Outkast3r09Best ResponseYou've already chosen the best response.1
\[y'=\sum_{n=1}^\infty c_nnx^{n1}\]
 one year ago

Outkast3r09Best ResponseYou've already chosen the best response.1
\[y''=\sum_{n=2}^\infty c_n(n)(n1)x^{n2}\]
 one year ago

TuringTestBest ResponseYou've already chosen the best response.0
oh I need a review on this bookmark*
 one year ago

Outkast3r09Best ResponseYou've already chosen the best response.1
i'm pretty sure i have it down so you can come check it after \[y''xy=\sum_{n=2}^\infty c_nn(n1)x^{n2}x\sum_{n=0}^\infty c_nx^n\]
 one year ago

Outkast3r09Best ResponseYou've already chosen the best response.1
\[\sum_{n=2}^\infty c_nn(n1)x^{n2}\sum_{n=0}^\infty c_nx^{n+1}\]
 one year ago

Outkast3r09Best ResponseYou've already chosen the best response.1
\[k=n2\] \[k+2=n\] \[\sum_{k=0}^\infty c_{k+2}(k+2)(k+21)x^k\sum_{n=0}^\infty c_nx^{n+1}=0\]
 one year ago

Outkast3r09Best 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 \[k=n+1\] \[k1=n\]
 one year ago

Outkast3r09Best ResponseYou've already chosen the best response.1
pull out one term k=0 of first \[2c_2+\sum_{k=1}^\infty c_{k+2}(k+2)(k+1)x^k\sum_{k=1}^\infty c_{k1}x^k\]
 one year ago

Outkast3r09Best ResponseYou've already chosen the best response.1
\[2c_2+\sum_{k=1}^\infty [c_{k+2}(k+2)(k+1)c_{k1}]x^k\]
 one year ago

Outkast3r09Best ResponseYou've already chosen the best response.1
since identity 0=0 the sum and \[2c_2=0\] \[c_2=0\]
 one year ago

Outkast3r09Best ResponseYou've already chosen the best response.1
\[c_{k+2}(k+2)(k+1)=c_{k1}\] \[c_{k+2}=\frac{c_{k1}}{(k+2)(k+1)}\]
 one year ago

Outkast3r09Best ResponseYou've already chosen the best response.1
for k=1,2,3,4,5,6......
 one year ago

Outkast3r09Best ResponseYou've already chosen the best response.1
k=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 \[c_6=\frac{c_3}{6*5)}=\frac{c_0}{6*5*3*2}\]
 one year ago

Outkast3r09Best ResponseYou've already chosen the best response.1
k=5 \[c_7=\frac{c_4}{7*6}=\frac{c_1}{7*6*4*3}\]
 one year ago

Outkast3r09Best ResponseYou've already chosen the best response.1
@TuringTest look correct so far?
 one year ago

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

experimentXBest ResponseYou've already chosen the best response.0
jeez ... i forgot all those stuffs. i need to review it myself.
 one year ago

TuringTestBest ResponseYou've already chosen the best response.0
hm... @Zarkon care to verify a DE series solution?
 one year ago

Outkast3r09Best ResponseYou've already chosen the best response.1
Is zarkon the computer on lol
 one year ago

experimentXBest ResponseYou've already chosen the best response.0
these standard equations power solutions look intimidating ...
 one year ago

Outkast3r09Best ResponseYou've already chosen the best response.1
\[y=c_0+c_1x+0+\frac{c_0}{3*2}x^3+\frac{c_1}{4*3}x^4+0+\frac{c_0}{2*3*5*6}x^6\] \[+\frac{c_1}{3*4*6*7}x^7+0......\]
 one year ago

Outkast3r09Best ResponseYou've already chosen the best response.1
\[y_1(x)=1+\frac{1}{2*3}x^3+\frac{1}{2*3*5*6}x^6...\] \[y_2(x)=x+\frac{1}{3*4}x^4+\frac{1}{3*4*6*7}x^7.......\]
 one year ago

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

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

Outkast3r09Best ResponseYou've already chosen the best response.1
only i left it not multiplied so i can creat a summation
 one year ago

experimentXBest ResponseYou've already chosen the best response.0
well, i guess you are right ... i never liked power series solution you know!!
 one year ago
See more questions >>>
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.