MATLAB Mathematics - SERC - Index of

5 Differential Equations
Note The demo emdenbvp contains the complete code for this example. The
demo uses subfunctions to place all required functions in a single M-file. To
run this example type emdenbvp at the command line. See “BVP Solver Basic
Syntax” on page 5-65 and “Solving BVP Problems” on page 5-68 for more
information.
1 Rewrite the problem as a first-order system and identify the singular
term. Using a substitution y 1 = y and y 2 = y′ , write the differential
equation as a system of two first-order equations
y 1 ′ = y 2
y 2 ′
2 5
= – --y
x 2 – y 1
The boundary conditions become
y 2 ( 0) = 0
y 1 ( 1) = 3 ⁄ 2
Writing the ODE system in a vector-matrix form
y 1 ′
y 2 ′
=
1
-- 0 0
x
0 – 2
y y 1 2
+
5
y 2 –y 1
the terms of Equation 5-2 are identified as
S
=
0 0
0 – 2
and
fxy ( , )
=
y 2
–y 1
5
5-82