dx = x + y - Los Angeles Mission College...(c) Sketch the curve π¦π¦(π₯π₯) if the initial...
Transcript of dx = x + y - Los Angeles Mission College...(c) Sketch the curve π¦π¦(π₯π₯) if the initial...
![Page 1: dx = x + y - Los Angeles Mission College...(c) Sketch the curve π¦π¦(π₯π₯) if the initial value is π¦π¦(0) = 0.5. (The curve does not have to be precise.) Author C. Henry](https://reader033.fdocuments.us/reader033/viewer/2022041721/5e4ed42bd192e728784a5524/html5/thumbnails/1.jpg)
1 dy . . - = -y - sm xdx
....
3 2
0
\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ '.' , ' . ' , β’ I " , " " " " .... ...... ..... ..... , "
/ / 1 1 / / /
- 1 I οΏ½ οΏ½ οΏ½ οΏ½ οΏ½ οΏ½ οΏ½ οΏ½
I I I I I I \ I I I I I I I I I I I 1.1 I I . I I . 1 I I I I I I I I , \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \
1 1 1 1 1 1 1 1 / / / / "" "" "" ""' / /
- 2 οΏ½ οΏ½ οΏ½ οΏ½ οΏ½ οΏ½οΏ½ οΏ½ οΏ½ j οΏ½ }.; οΏ½ ;οΏ½ οΏ½ οΏ½I I I I I I I I I 1 1 1 / / / 1 / 1I I I I I I I I I I 1 1 1 1 1 1 1 1
-οΏ½3 -2 - 1 0 2
dy 2. dx = x + y
- - / / / / 1 1 1- - - / / / / / /
2 ""-= ::: :::: οΏ½ οΏ½ οΏ½ οΏ½ οΏ½
x
I I I I I I II I I I I I I lei I . I Ie I I I I I I I I I I I I I I I I I I I I I I I I I I / / 1 1 1 1 1 1 1/ / 1 1 1 1 1 1 1/ / / / / 1 1 1 1
3
.... o οΏ½οΏ½οΏ½οΏ½οΏ½-+--οΏ½οΏ½+Β₯οΏ½οΏ½
- 1
- 2
3 dy . . - = y - sm xdx
2
I I I I I I I I I I I I I I I I I I Ie I lei I I I I I I I I I I I I I I I I I I I I
x
I I I I 1 I 1 1 11 1 / / / / 1 1 1I I ,. / / /., / I / / / / / / / / /
/ I I I I I I / I / 1 1 1 1 1 1 / // / / I / / / / .;/οΏ½-οΏ½οΏ½
- 1 " ..... ...... ...... ..... , , '
-2 \ οΏ½ οΏ½οΏ½ οΏ½ οΏ½οΏ½ οΏ½ οΏ½ \ \ \ \ \ \ \ \ \\ \ \ \ \ \ \ \ \ -οΏ½3 -2 - 1 0
x 2
3
3
dy 4. - = x - ydx
2
- 1
-2 : :: :': :: ;οΏ½ οΏ½ j - - - / / / / 1 1- - / / / / 1 1 1
-οΏ½3 -2 - 1
dy 5. - = Y - x + 1dx
I I 2 I I I I
οΏ½.οΏ½ I I .... 0
I I
o 2 x
- - - ..... , ' \ \ \ ./ - - ..... , ' \ \ \ \
- 1
- 2
- 1
dy 6. - = x - y + ldx
2
\ I I I I I \ \ \ I I I I 1 \ ' 1 .1 I . \ \ . ' \ \ \ \ \ \ \ \ , \ \ \ \ \ \ \ " \ \ \ \ \ \ " " .....
o x
- ..... " " \ '.' \ \ ...... , ' \ \ \ \ \ \ " \ \ \ \ \ \ \, \ \ \ \ \ \ \ \ , 1Β· 1 I I e.. I I , I I I I I \ \ I , \ I I I I \ I I
2
, ... , \ \ ' , ...... -\ \ \ \ ' , ..... - - ./
\ ,
- 1 : : _ _ οΏ½ ; οΏ½ οΏ½ j- - - / / / 1 1 1
-2 :: ; οΏ½οΏ½ οΏ½ οΏ½οΏ½ οΏ½ οΏ½ / / / / 1 1 1 1 /./ / I I I I I I I
-οΏ½3 -2 - 1 0 x
3
3
Differential Equation - Spring 2015 - Classwork 1Instructor: Emil Sargsyan
Name: _____________________________
In problems 1-6 one of the solutions of the differentialequation is given. Sketch additional solutions through the given points.
![Page 2: dx = x + y - Los Angeles Mission College...(c) Sketch the curve π¦π¦(π₯π₯) if the initial value is π¦π¦(0) = 0.5. (The curve does not have to be precise.) Author C. Henry](https://reader033.fdocuments.us/reader033/viewer/2022041721/5e4ed42bd192e728784a5524/html5/thumbnails/2.jpg)
7. Suppose the differential equation ππππππππ
= ππ(π₯π₯,π¦π¦) has ππ(π₯π₯) as its solution. We know that the slope of the graph of ππ at the point (π₯π₯,π¦π¦) is the product of π₯π₯ and π¦π¦. What is ππ(π₯π₯,π¦π¦)?
8. (a) Sketch the slope field of the differential equation ππππππππ
= π¦π¦. The vectors donβt have to be precise, and be sure to produce the vectors at the positions (0,0), (1,0), (0,1), (-1,0), (0,-1),(0,3), (3,0), (0,-3), (-3,0).
(b) Solve the differential equation π¦π¦β² = π¦π¦
(c) Sketch the curve π¦π¦(π₯π₯) if the initial value is π¦π¦(0) = 0.5.
(The curve does not have to be precise.)