University of Leeds
DIFFERENTIAL EQUATIONS
MATH1970
Model solutions to Examples 1
Identify the dierential equation that corresponds to the given directional eld. (a) (b) (c) (d) 1. (e) (f ) (g) (h) (i) (j) y = 2y 1 y =2+y y =y2 y = y(y + 3) y = y(y 3) y =
University of Leeds
MATH1970
DIFFERENTIAL EQUATIONS
Model solutions to Examples 5
Find a value of for which the column vector
x(t) =
1.
1 7t
e
is a solution of the matrix dierential equation
d
dt
x1
x2
1 12
3 1
=
If x1 (t) = e7t and x2 (t) = e7t then
We n
MATH1970-01
MATH1970-01
Only approved basic scientic calculators may be used
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c UNIVERSITY OF LEEDS
Examination for the Module MATH1970
(August 2008)
Di
University of Leeds Ordinary Differential Equations
MATH1970
Examples 2
Hand in your solutions by 5pm on Thursday, 26th February.
1. In 1838 the Belgian biologist Verhulst used the following ODE to study population growth: dy = y( y), dt where and are pos