Honors AP Calculus / Mr. Hansen	Name: ____________________
12/15/2009

Six In-Class Differential Equation Problems

Instructions For each problem, you should do the following: (a) compute an exact general solution, if possible (b) compute an exact particular solution, if possible (c) plot the slope field by hand (using SLOPEFLD to check) (d) compute a set of Euler’s method estimates (ordered pairs) (e) use the EULER program to check your work in (d), if possible (f) overlay the Euler’s method y values and exact solution on your slope field sketch (g) if applicable, compare the Euler’s estimates against the exact solution’s y values. Neatness counts!
1.	Initial condition: (4, 1.5). Estimate y(3.5) by using 5 Euler steps.
2.	Given the following data table, use curve fitting to develop a suitable model for Then, use 2 Euler steps from the given initial condition for (x, y) to estimate y(2.1).
		x		y
		----------	----------	----------
		1.1	8	2
		1.2	9
		1.3	11
		1.4	14
		1.6	16
		1.9	19
3.	Initial condition: (1, 1). Estimate y(1.4) by using at least 4 Euler steps.
4.	Estimate y(4.2) using an initial condition of (4, 1) and 2 Euler steps. Then estimate y(4.2) using an initial condition of (4, −1) and 2 Euler steps.
5.	Initial condition: (0.1, 3.4). Estimate y(0.3) with at least 2 Euler steps. Warning: You must find a way to work around calculator failures.
6.	Given: is proportional to y, initial conditions (3, 2) and (4, 1.8). Estimate y(5) with at least 2 Euler steps.