This preview shows page 1. Sign up to view the full content.
Unformatted text preview: M427 K
PRACTICE EXAM 1
Directions: This exam is meant to suggest the kind, di culty, and
number of problems on the real exam. Note that topics covered in the
course, but not included on this practice exam, still might appear on
the real exam. Set aside 50 minutes during which you can work on this
exam without interruption. Refer to no books, notes, or calculators
while working on the exam. This will give you a sense of your level of
preparation for the real exam. 1.(20pts) Solve the I.V.P.
(3x2 2xy + 2) + (6y 2 x2 + 3) dy
dx y (0) = 5. 2.(20pts) Using 0 = 0, ﬁnd the next two Picard iterates (using the
method of successive approximation) for the I.V.P.
y 0 = 2t(1 + y ), y (0) = 0. 3.(20pts) Solve the I.V.P.
y 00 + 9y = 0, y (0) = 1, y 0 (0) = 0. 4.(20pts) Find the general solution of
y 00 + 4y 0 5 y = e 2t . 5.(20pts) The equation
ty 00 (t + 1)y 0 + y = 0, t > 0 has the solution y1 = et . Find a fundamental set of solutions. 1 ...
View Full Document