Math 250a (Fall ‘07) - Homework 9 extra problems
1. For each of the following differential equations, before you plot the slope
field first determine which of the three possible symmetries the slope field
has and what this tells you about the solutions. Then plot the slope field
and some solutions to check your answer. (The three possible symmetries are
reflection in the x-axis, reflection in the y-axis and reflection in the origin.)
(a)y3y0=x2
(b)y0=y
2x
(c)y0= sin(xy)
2. Consider the dif eq
dy
dx =f(x)h(y)
For each of the following cases determine which of the three possible symme-
tries the slope field has and what this tells you about the solutions. Check
your answer by making up and fand hfor each case and plotting the slope
field.
(a) f and h are both even functions
(b) f and h are both odd functions
(c) f is an odd function and h is an even function
(d) f is an even function and h is an odd function
3. Suppose that Yis a solution to the differential equation
dY
dx =Y2(1 −Y) (1)
Now consider the differential equation
dy
dx = 2y2(5 −y) (2)
By considering functions of the form aY (bx) where aand bare constants,
express y(x) in terms of Y(x).
4. The differential equation
du
dx = (1 + u)(2 + u)
1
