1. A direction field for the differential equation y' = y(l - ;y2)
is shown.
(a) Sketch the graphs of the solutions that satisfy the given
initial conditions.
(i) y(0) = 1 (ii) y(0) _ -1
3-6 Match the differential equation with its direction field
(labeled 1 -IV ). Give reasons for your answer.
3. y' = 2 r 4 . Y' = x(2 - y)
(iii) y(0) _ -3 (iv) y(0) = 3
(b) Find all the equilibrium solutions.'
-
=0
5. y'=x+y-
b.
14tL1 t_^(^Z. yy
= sin x sin y
II
/////// -- \\\\\
///////- ^^V\\V\
/ / / / / / /= . N A v V \ \
\\\VAN
-///////
\\\\\\\
/
/
/
/
/
/
1/ l-43
/
/
/
/
/
U
-2
/
///////
/ l I l I I l I
IV
4
2. A direction field for the differential equation y' = x sin v is
shown.
(a) Sketch the graphs of the solutions that satisfy the given
initial conditions.
(i) Y(0) = 1 (ii) y(O) = 2 (iii) Y(0) = ar
//////// ////////
-2
(iv) y(O) = 4 (v) y(0) = 5
01
2
(b) Find all the equilibrium solutions. XS W -
Sys.
- 0
:z- J ^' - x Cz-S)
^ew^ e `^ el w`^` tHS t^ = Z- ^ ^o
-3
OL
4964^iv
1/`'', r. t,
5 - t ^T-- G^,a ^^