University of London The London School of Economics and Political Science
MA 209

Winter 2014
[SE
Summer 2009 examination
MA209
Differential Equations
Half Unit
Suitable for all candidates
Instructions to candidates
Time allowed: 2 hours
This paper contains 5 questions. You may attempt as many questions as you wish,
but only your best 4 answers wi
University of London The London School of Economics and Political Science
MA 209

Winter 2014
Summer 2008 examination
MA209
Differential Equations
Half Unit
2007/2008 syllabus only — not for resit candidates
Instructions to candidates
Time allowed: 2 hours
This paper contains 5 questions, You may attempt as many questions as you wish,
but only you
University of London The London School of Economics and Political Science
MA 209

Winter 2014
Differential Equations
MA 209
2007/08
Solutions 2008 Exam
1
(a) (i)
A xed point of the differential equation z = (z + C )2 (z2 C ) occurs when z = 0,
hence when (z + C )2 (z2 C ) = 0. This gives z = C or z2 = C.
If C < 0, then we have only one xed point
University of London The London School of Economics and Political Science
MA 209

Winter 2014
Summer 2007 examination
MA209
Differential Equations
Half unit
2006/2007 syllabus only — not for resit candidates
Instructions to candidates
Time allowed: 2 hours
This paper contains 5 questions. You may attempt as many questions as you wish,
but only you
University of London The London School of Economics and Political Science
MA 209

Winter 2014
Summer 2006 examination
Differential Equations
(Half Unit)
Suitable for all candidates
Instructions to candidates
Time allowed :
2 hours.
This exam contains 5 questions. You may attempt as many questions as you wish,
but only your best 4 questions will co
University of London The London School of Economics and Political Science
MA 209

Winter 2014
Differential Equations
2005/06
MA 209
Solutions 2006 Exam
1
(a) (i)
x+
is continuous for all (t, x) R2 with t = . So
2 (t )
by a result from the lectures, provided the initial value is given for some t0 = , a
solution exists for all initial values.
The fu
University of London The London School of Economics and Political Science
MA 209

Winter 2014
Summer 2005 examination
MA 209
Differential Equations
(Half Unit)
Suitable for all candidates
Instructions to candidates
Time allowed: 2 hours.
This exam contains 5 questions. You may attempt as many questions as you wish,
but only .your best 4 questions
University of London The London School of Economics and Political Science
MA 209

Winter 2014
Differential Equations
MA 209
2004/05
Solutions 2005 Exam
1
(a) (i)
A xed point of x = (x 1)2 (x + 2) (x K) occurs when x = 0. This immediately
gives x = 1, x = 2 or x = K.
If K > 1, then the order of xed points is 2, 1, K. For x > K we have x > 0; for
1
University of London The London School of Economics and Political Science
MA 209

Winter 2014
Summer 2010 examination
MA 209
Dierential Equations
(Half Unit)
Suitable for all candidates
Instructions to candidates
Time allowed :
2 hours.
This examination paper contains 5 questions. You may attempt as many questions
as you wish, but only your BEST 4