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Outkast3r09
Group Title
Find two power series solutions of the given differential equation about the ordinary point x=0: y''xy=0
 2 years ago
 2 years ago
Outkast3r09 Group Title
Find two power series solutions of the given differential equation about the ordinary point x=0: y''xy=0
 2 years ago
 2 years ago

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

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

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

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

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

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

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

Outkast3r09 Group TitleBest 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 \[k=n+1\] \[k1=n\]
 2 years ago

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

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

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

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

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

Outkast3r09 Group TitleBest 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 \[c_6=\frac{c_3}{6*5)}=\frac{c_0}{6*5*3*2}\]
 2 years ago

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

Outkast3r09 Group TitleBest ResponseYou've already chosen the best response.1
\[c_8=c_5=0\]
 2 years ago

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

TuringTest Group TitleBest 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
 2 years ago

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

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

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

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

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

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

experimentX Group TitleBest 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
 2 years ago

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

Outkast3r09 Group TitleBest ResponseYou've already chosen the best response.1
thats what i have
 2 years ago

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

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