MA2001N Differential Equations
Example Sheet 2
(a) Reducible forms
(i)
Use the substitution, v y , to find the general solution of the
following equations:
(1)
(2)
(ii)
x 3 y 4 x 2 y 1 ,
y 2 y x
x 0
Solve each of the following initial value problems, comp
MA2001N Differential Equations
Example Sheet 6
Examples of the solution of Eulers Equation
In the questions that follow, apply the general solution procedure, as outlined in section 6
of the notes for week 6, to the specific examples given.
Answers are gi
MA2001N Differential Equations
Example Sheet 3
Reduction of Order I: Analytical Examples
(1)
If y1 is a solution of the homogeneous form of
y p( x) y q ( x) y g ( x ) ,
(A)
W
y 2 y1 2 dx ,
y1
(B)
show that
where
W exp(
p( x) dx)
,
is also a solution of th
MA2001N Differential Equations
Lecture Notes for Weeks 3, 4 and 5
[5.
General 2nd order, linear odes
(including)
5.2 Solution by the general method
of Reduction of Order]
5.
General 2nd order, linear odes
The most general form for a 2nd order, linear ode
MA2001N Differential Equations
Example Sheet 1:
Revision Sheet
(a) Revision of Integration Techniques
To solve differential equations it is often necessary to use certain elementary
integration techniques. So, it is a good idea to do some revision on sele