dx = x + y - los angeles mission college...(c) sketch the curve 𝑦𝑦(𝑥𝑥) if the initial...

1 dy . . - = -y-smx dx 3 2 0 \ \ \ \ \ \ \ \ \ \ \\\\\\\ \ '.' , ' . ' , • I " ," " " " . . , " / / 1 1// / -1 I� �� 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 � � � � � � � � � j � }; �;� � � IIIIIIIII 1 1 1/ // 1 / 1 I I II I IIII I 1 1 1 1 1 1 1 1 -�3 -2 -1 0 2 dy 2. dx = x + y - -/ / / / 1 1 1 - - -/ / // / / 2 : � � � � � x I I I I I I I I I II I I I l 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 I I / /1 1 1 1 1 1 1 / /1 1 1 1 1 1 1 / / / / / 1 1 1 1 3 o � -1 -2 3 dy . . - = y -smx dx 2 I I I I I I I I I I I I I I I I I I I l 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 1 1 1 / / / / 1 1 1 I I ,/ / / / I / / / //// // / I I I I I I / I / 1 1 1 1 1 1 / / / // I / / // � -1 " . . , ,' -2 \ � �� \ \\\\\\ \\ \ \ \ \ \ \ \ \ \ -�3 -2 -1 0 x 2 3 3 dy 4. -=x -y dx 2 -1 -2 :: ;� �j - - -/ / / / 1 1 - -/ / / / 1 1 1 -�3 -2 -1 dy 5. - = Y -x+ 1 dx I I 2 I I I I �.� I I 0 I I o 2 x - - - . , '\\ \ - - . , ' \\ \\ -1 -2 -1 dy 6. -=x -y+l dx 2 \ I I I I I \ \ \ I I I I 1 \ ' 1 .1 I. \ \ .' \ \ \ \ \ \ \ \ , \\ \ \\ \\ " \ \ \ \ \ \ " " . o x - . " " \ '.' \ \ , ' \\ \\ \ \ " \\ \\ \\\ , \ \ \ \ \ \ \ \ , 1 · 1 I I e. I I , I I I I I \ \ I , \ I I I I \ I I 2 , . , \ \ ' , - \\ \\', . - - \ , -1 : : _ _ �; � � j - - -/ / / 1 1 1 -2 ;� � � � � �� / / / / 1 1 1 1 / / I I I I I I I -�3 -2 -1 0 x 3 3 Differential Equation - Spring 2015 - Classwork 1 Instructor: Emil Sargsyan Name: _____________________________ In problems 1-6 one of the solutions of the differential equation is given. Sketch additional solutions through the given points.

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Page 1: dx = x + y - Los Angeles Mission College...(c) Sketch the curve 𝑦𝑦(𝑥𝑥) if the initial value is 𝑦𝑦(0) = 0.5. (The curve does not have to be precise.) Author C. Henry

1 dy . . - = -y - sm xdx

....

3 2

\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ '.' , ' . ' , • I " , " " " " .... ...... ..... ..... , "

/ / 1 1 / / /

- 1 I � � � � � � � �

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 � � � � � �� j � }.; � ;� � �I 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

-�3 -2 - 1 0 2

dy 2. dx = x + y

- - / / / / 1 1 1- - - / / / / / /

2 ""-= ::: :::: � � � � �

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

.... o ��-+--��+¥��

- 1

- 2

3 dy . . - = y - sm xdx

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

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 / / / / .;/�-��

- 1 " ..... ...... ...... ..... , , '

-2 \ � �� \ \ \ \ \ \ \ \ \\ \ \ \ \ \ \ \ \ -�3 -2 - 1 0

x 2

dy 4. - = x - ydx

- 1

-2 : :: :': :: ;� � j - - - / / / / 1 1- - / / / / 1 1 1

-�3 -2 - 1

dy 5. - = Y - x + 1dx

I I 2 I I I I

�.� I I .... 0

I I

o 2 x

- - - ..... , ' \ \ \ ./ - - ..... , ' \ \ \ \

- 1

- 2

- 1

dy 6. - = x - y + ldx

\ I I I I I \ \ \ I I I I 1 \ ' 1 .1 I . \ \ . ' \ \ \ \ \ \ \ \ , \ \ \ \ \ \ \ " \ \ \ \ \ \ " " .....

o x

- ..... " " \ '.' \ \ ...... , ' \ \ \ \ \ \ " \ \ \ \ \ \ \, \ \ \ \ \ \ \ \ , 1· 1 I I e.. I I , I I I I I \ \ I , \ I I I I \ I I

, ... , \ \ ' , ...... -\ \ \ \ ' , ..... - - ./

\ ,

- 1 : : _ _ � ; � � j- - - / / / 1 1 1

-2 :: ; �� / / / / 1 1 1 1 /./ / I I I I I I I

-�3 -2 - 1 0 x

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 𝑦𝑦(𝑥𝑥) if the initial value is 𝑦𝑦(0) = 0.5. (The curve does not have to be precise.) Author C. Henry

7. Suppose the differential equation 𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑

= 𝑓𝑓(𝑥𝑥,𝑦𝑦) has 𝑔𝑔(𝑥𝑥) as its solution. We know that the slope of the graph of 𝑔𝑔 at the point (𝑥𝑥,𝑦𝑦) is the product of 𝑥𝑥 and 𝑦𝑦. What is 𝑓𝑓(𝑥𝑥,𝑦𝑦)?

8. (a) Sketch the slope field of the differential equation 𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑

= 𝑦𝑦. The vectors don’t 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 𝑦𝑦′ = 𝑦𝑦

(The curve does not have to be precise.)

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