APMA 2101 Problem Set #3 Sample Solution Set
(due 20 February 2007)
Chapter 2: Review Problem
For
x(y)
, we have
dx/dy + x = y
, with integrating factor
exp(y)
.
Integrating both sides and using integration by parts
once on the right-hand side gives
x(y)=c*exp(-y)+y-1
.
Section 2.4: Exact ODEs
Section 6.1: The Euler Method
11. The exact solution, following the hint, is
u(x) = tan(x+c)
, or with the initial condition and a return to the original
variables,
y(x)=tan(x+
π
/4)+1-x
.
Section 6.2: The Runge-Kutta Method

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