Toronto Math Forum

MAT244-2018S => MAT244––Home Assignments => Web Bonus Problems => Topic started by: Victor Ivrii on January 20, 2018, 09:49:36 AM

Title: Web bonus problem--Week 3
Post by: Victor Ivrii on January 20, 2018, 09:49:36 AM
a. Find the general solution of
$$
y'+2\cot(t)y=\cos(t).
$$
b. Find solution, which is defined on $(-\infty,\infty)$;
c. Find solution, which is defined on $(-\infty,\infty)$ and periodic.
Title: Re: Web bonus problem--Week 3
Post by: Wenzhe Xu on January 22, 2018, 01:42:07 PM
Here is my attempt, but I'm confusing about question b and c, is my thought right?

(http://i65.tinypic.com/2qiaccw.jpg)
Title: Re: Web bonus problem--Week 3
Post by: Runcong Wu on January 22, 2018, 01:47:54 PM
Here, the last one has the wrong image code
(http://i67.tinypic.com/k3nip3.png)
Title: Re: Web bonus problem--Week 3
Post by: Victor Ivrii on January 22, 2018, 01:53:50 PM
Looks OK. Could you type it?
Title: Re: Web bonus problem--Week 3
Post by: David Chan on January 22, 2018, 02:59:02 PM
My (typed) solution:
(https://i.imgur.com/7MjaNpE.png)
Title: Re: Web bonus problem--Week 3
Post by: Rui Zhu on January 22, 2018, 07:33:07 PM
Hi, here is my solution
(https://imgur.com/pdhr4hA.jpg)
Title: Re: Web bonus problem--Week 3
Post by: Junya Zhang on January 22, 2018, 08:18:11 PM
(http://i68.tinypic.com/2hxufx2.jpg)
(http://i66.tinypic.com/33ligzk.jpg)
Title: Re: Web bonus problem--Week 3
Post by: Yuying Zhai on January 22, 2018, 08:33:30 PM
Hello, here is my solution.
(https://i.imgur.com/bLGelce.jpg)
Title: Re: Web bonus problem--Week 3
Post by: Kaiman Chen on January 22, 2018, 08:45:01 PM
Here is my final answer for week 3 bonus problem(https://imgur.com/00ZZCd1.jpg)
Title: Re: Web bonus problem--Week 3
Post by: Xiangji Kong on January 22, 2018, 09:09:23 PM
(https://i.imgur.com/g9JMQHW.jpg)
Title: Re: Web bonus problem--Week 3
Post by: Seunghyun Park on January 22, 2018, 09:13:53 PM
(https://imageshack.com/a/img924/3554/wVaoth.png)
Title: Re: Web bonus problem--Week 3
Post by: Xu Bai on January 22, 2018, 09:13:58 PM
(http://forum.math.toronto.edu/Users/jasonbai/Desktop/53836618264__B3129D99-7236-4576-91D9-553471D77C98.png)

my solution to week3's problem
Title: Re: Web bonus problem--Week 3
Post by: Zhiqing Pan on January 22, 2018, 09:25:02 PM
(https://imgur.com/o77o44u.jpg)
Title: Re: Web bonus problem--Week 3
Post by: Yufei Cai on January 22, 2018, 09:31:11 PM
Here is my solution.
(https://i.imgur.com/URLxr3i.jpg)
Title: Re: Web bonus problem--Week 3
Post by: Vivian Ngo on January 22, 2018, 09:47:55 PM
(https://scontent.fybz2-1.fna.fbcdn.net/v/t35.0-12/27265677_10213528247031936_1305947941_o.jpg?oh=a95e4ef8e7887a9b22b5e2746fad679a&oe=5A68D221)
Title: Re: Web bonus problem--Week 3
Post by: Catherine Yue on January 22, 2018, 10:12:39 PM
a. y=sint/3+c/(sint)^2
b. y=sint/3
c. y=sint/3
Title: Re: Web bonus problem--Week 3
Post by: Tiange Gao on January 22, 2018, 10:19:26 PM
The attached is my solution. Thank you
(https://s17.postimg.org/vv9btu3in/We_Chat_Image_20180122220512.jpg)
(https://s17.postimg.org/3wjrgk6nj/We_Chat_Image_20180122220550.jpg)

Title: Re: Web bonus problem--Week 3
Post by: Kaiying Jiang on January 22, 2018, 10:27:45 PM
The final answer is:(detail steps are in attachment)
a. y=1/3*sint+c*[sin(t)]^(-2)
b. When c=0, y=1/3*sin(t)
c. When y=1/3*sin(t), definable on negative infinity to positive infinity, and periodic of 2∏, which is 2 times of Pi.

(https://imgur.com/ucHek9H.jpg)
Title: Re: Web bonus problem--Week 3
Post by: Shirley Wen on January 22, 2018, 10:30:57 PM
(https://imgur.com/ArUOkzh.jpg)
Title: Re: Web bonus problem--Week 3
Post by: Kaiying Jiang on January 22, 2018, 10:37:11 PM
(https://imgur.com/a/Hy9lR.jpg)
Title: Re: Web bonus problem--Week 3
Post by: Zhiman Tang on January 22, 2018, 10:51:25 PM
(https://i.imgur.com/DM9G6cf.jpg?1)
Title: Re: Web bonus problem--Week 3
Post by: Yilin Ye on January 22, 2018, 11:04:08 PM
a)
y′+2cot(t)y=cos(t).
p(t)=2cot(t)
I=e^∫2cot(t)dt
 =e^2∫cos(t)/sin(t)dt
 =e^2ln|sin(t)|
 =e^ln|sin(t)|^2
 =sin(t)^2

sin(t)^2y′+2cot(t)sin(t)^2y=cos(t)sin(t)^2

(sin(t)^2y)'=cos(t)sin(t)^2
sin(t)^2y=∫cos(t)sin(t)^2dt
              =1/3sin(t)^3+c
            y=1/3sin(t)+csin(t)^-2

b)let c=0  y=1/3sin(t)
c)let c=0  y=1/3sin(t)
Title: Re: Web bonus problem--Week 3
Post by: Shiyi Hou on January 22, 2018, 11:12:03 PM
(http://i66.tinypic.com/2liiyvc.jpg)
Title: Re: Web bonus problem--Week 3
Post by: Yuming Song on January 22, 2018, 11:20:42 PM
(https://imgur.com/VjEW0Xd.jpg)
Title: Re: Web bonus problem--Week 3
Post by: Jiayun Huang on January 22, 2018, 11:28:08 PM
(https://imgur.com/a/BPEGJ.jpg)
Title: Re: Web bonus problem--Week 3
Post by: Ge Shi on January 22, 2018, 11:35:40 PM
(http://i1347.photobucket.com/albums/p709/shigevertas/WechatIMG2_zpsi8ssxkgk.jpeg)
Title: Re: Web bonus problem--Week 3
Post by: Yatong Yu on January 22, 2018, 11:43:54 PM
(http://i1259.photobucket.com/albums/ii541/thhsxhl/IMG_0287_zpssrjwdgfd.jpg)
Title: Re: Web bonus problem--Week 3
Post by: Ge Shi on January 22, 2018, 11:49:46 PM
I already uploaded my solution in reply#30. Sorry for posting the message twice...
Title: Re: Web bonus problem--Week 3
Post by: Jiayuwjy Wu on January 22, 2018, 11:50:22 PM
(http://i1378.photobucket.com/albums/ah115/tobejy/WechatIMG225_zpshwfpnztr.jpeg)
Title: Re: Web bonus problem--Week 3
Post by: Roberto Hechen on January 22, 2018, 11:57:21 PM
(https://imgur.com/j39Vs4Q.jpg)
Title: Re: Web bonus problem--Week 3
Post by: Silvia Shiyan Chen on January 23, 2018, 12:01:54 AM
(https://imgur.com/a/EvrWX.jpg)
Title: Re: Web bonus problem--Week 3
Post by: Qingyuan Chen on January 23, 2018, 12:03:32 AM
(https://imgur.com/XePaJ6m.jpg)
Title: Re: Web bonus problem--Week 3
Post by: Biyu Li on January 23, 2018, 12:07:08 AM
Hi, here's my answers to bonus questions. Thank you~
(https://outlook.office.com/owa/service.svc/s/GetAttachmentThumbnail?id=AAMkADQ2NGRjZDJmLWNiYmMtNDg4NS04OWZjLWZiMGRmYzQ3NTQwMQBGAAAAAABKkUHOttDIS7GLrReQieiaBwAbaaUxkwvSSaJMW7e%2BAASOAAAAAAEMAAAbaaUxkwvSSaJMW7e%2BAASOAACsGrlyAAABEgAQAFWUnEwRZJxFhZ3h7FPQMqM%3D&thumbnailType=2&X-OWA-CANARY=Lg5_zdQI1kmU--lXZgqtf8A7NL0fYtUYy3wcFV4wGl-Nw0ZaGbxm5sz8uitDiqjs7RDJUB0fsu8.jpg)
Title: Re: Web bonus problem--Week 3
Post by: Silvia Shiyan Chen on January 23, 2018, 12:21:36 AM
(https://mail-attachment.googleusercontent.com/attachment/u/0/?ui=2&ik=b4e13e569d&view=att&th=161216a84bb00cf0&attid=0.1&disp=safe&zw&saddbat=ANGjdJ_EL2qZUslCC_MXkKKNkcLMtsB3N-RPLBDQ4n6NQgHYABEe7RfbYaBc0irL12hiiSj-sTimGrjwxrmhojlUNv9r0zvhoWTf0NHQH9kNelzuhHxsr4IkdNKZ45lCu5OyiZmxGXJ9mlKCQLDCIoNuLsdcG-6HdUCCQDqnh07mLHjx0WZ-hc4N1zVoGg5FhjcTeykp-DwIFv2iLvyuuZ-NdQ1cYIuU66hQ_ydF6idDUHZFARBUnmK77vRo4swbHyZUuTX_T-3LKKKY_LlkWj6WTjMqQMVwFEWv-oDO527s4OaXDc7SOeE5nzeNnIC65FTWuQ9WLV3s5IgG3h447uAM6jMk-S_qsMUVwRuECUOKLE5YDGGZ-KGOhbIu3_M7OZ-hcP_0D4lBsjqgZF__hojLYIZ8m0NM4H2on6DfKj59YO7mQq3O1DA-oD-WecxB0iZ82is8b6TpqTpX4QbCY4OpiZRNtEJy-gk4UiQoaVCCYz756vwn0anuU_mM3xe6ESXqC5ieJfbmokcZRFnq7OyedLbNgPlULjM4Ljth_kqTbLLbVHMbSHXy1ETdB48i9ANvGkpMBFPfYUz3AMuopvngkOqfVvLgv-aCJykDGQ,https://mail.google.com/mail/u/0/)
Title: Re: Web bonus problem--Week 3
Post by: Vicky Liu on January 23, 2018, 12:35:42 AM
(https://imgur.com/WKjMnvo.jpg)
Title: Re: Web bonus problem--Week 3
Post by: Zihao Yuan on January 23, 2018, 12:36:58 AM
(https://imgur.com/QNKVZ8Z.jpg)
(https://imgur.com/q0S6NXY.jpg)
Title: Re: Web bonus problem--Week 3
Post by: Yingying Zheng on January 23, 2018, 12:40:39 AM
(https://s9.postimg.org/4hmh2obsf/1520676482.jpg)
Title: Re: Web bonus problem--Week 3
Post by: Yuling Chen on January 23, 2018, 12:43:50 AM
(http://i1036.photobucket.com)
Title: Re: Web bonus problem--Week 3
Post by: Yuling Chen on January 23, 2018, 12:46:04 AM
(http://[URL=http://s1036.photobucket.com/user/YulingChen/media/2018-01-23_zpsqewy3fyx.png.html][IMG]http://i1036.photobucket.com/albums/a443/YulingChen/2018-01-23_zpsqewy3fyx.png)[/URL][/img]
Title: Re: Web bonus problem--Week 3
Post by: Yuling Chen on January 23, 2018, 12:46:43 AM
(http://i1036.photobucket.com/albums/a443/YulingChen/2018-01-23_zpsqewy3fyx.png)
Title: Re: Web bonus problem--Week 3
Post by: Mengyang Li on January 23, 2018, 12:49:00 AM
(https://imgur.com/k3i3yZM.jpg)
Title: Re: Web bonus problem--Week 3
Post by: ZHITONG,LI on January 23, 2018, 01:12:58 AM
Here is the solution for the question:
(https://photos.smugmug.com/Week3/i-QM3NnJq/0/99585bea/XL/week3bouns-XL.png)
Title: Re: Web bonus problem--Week 3
Post by: Yingyun He on January 23, 2018, 01:17:18 AM
(http://i1356.photobucket.com/albums/q722/hyylor/IMG_0838_zpsx1s4kgbr.png) (http://s1356.photobucket.com/user/hyylor/media/IMG_0838_zpsx1s4kgbr.png.html)
Title: Re: Web bonus problem--Week 3
Post by: Yulun Wu on January 23, 2018, 01:19:39 AM
here is my solution
(https://i.imgur.com/UNCIH34.jpg)
Title: Re: Web bonus problem--Week 3
Post by: yongwen tan on January 23, 2018, 02:05:44 AM
(https://imgur.com/2aaczTj.jpg)
Title: Re: Web bonus problem--Week 3
Post by: Victor Ivrii on January 23, 2018, 05:10:32 AM
When I wrote "type" I meant type on forum. Like I do:
$$y'+2\cot(t)y=\cos(t)$$,
then
$$I=\exp\Bigl(2\cot(t)\,dt\Bigr)=\exp \bigl(2\ln \sin(t)\bigr)=\sin^2(t)$$
and so on, not to put image (even typed) on forum.

Don't cut lines too short... Also $\exp $, $\cos$ etc should be upright (in $\LaTeX$ it is \exp, \cos).

No external images! Post attachments
Title: Re: Web bonus problem--Week 3
Post by: Victor Ivrii on January 23, 2018, 05:22:22 AM
Usually web bonus is given to the first poster (or may be for improvements if the first poster did not get everything right). This time I was more generous. But not infinitely. Bonus got first 5 or so