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Unformatted text preview: Quiz #1 - June 15, 2009 1. (8) Substitute y = 6” into y” — y’ — 2y 2 0 to determine all values of the
constant 7" for which y = e”? is a seiution of the differential equation. (1)) What is the order of the differential equation? (c) Is the differential equation linear
or nonlinear? (ﬂ éubbiﬁjﬂ 1 -"=YLW
\fnr Vii/2L!” Vie 1" ya,“ “° 99‘”: O
mi 2. §1.5, #42: Suppoae that a falling hailstone with density 6 = 1 starts from
rest with negligible radius 7" m 0. thereafter its radius is 7‘ = kt (k is a constant)
as it grows by accretion during its fall. Use Newton’s second law -— according
to which the net force F(t) acting on a possibly variabie mass m(t) equais the
time rate of change dp/dt of its momentum p = my w to solve the initial value I probiem d gimme» : m(t)g, M0) = 0a where m is the variable mass of the hailstone, v = dy/dt is its velocity, and
the positive y-axis points downward. Then shew that dv/dt = 51/4. Thus the
hailstone falls as though it were under One—fourth the inﬂuence of gravity! We, ﬂair-k with ...
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- Spring '07