# math285: the week of september 15

Review sections 2.2, 2.4, 2.6 of the textbook (Edwards and Penney). Listen to the video lectures.

Additional reading (highly recommended!): chapter 1 of Ordinary differential equations : a practical guide by
Bernd J. Schroers (CUP, 2011).

Homework (due by Monday, 9.24):

1. Sketch the vector fields for each value of the parameter; indicate equilibria and their stability:

$\dot{y}=y^3-3y+a, a=-3,0,3;$

2. Find the three consecutive Picard iterations for
$\dot{y}=y^2, y(0)=1.$
Solve the differential equation; compare the Taylor expansion of the result with the third Picard iteration.
3. Can different solutions of the following differential equations touch at a point $$(x,y)$$?

1. $y’=x+y^2;$
2. $y”=x+y^2;$
3. $y”’=x+y^2;$

### 2 Responses to math285: the week of september 15

1. Michael September 20, 2014 at 4:15 pm #

Could you clarify question 3? I’m not really sure what to do.

• yuliy September 22, 2014 at 12:20 am #

Two solutions touch at a point if they have the same value (y) and the same derivative (slope).