prof TSteele 001
Assignment 1.1-existence uniqueness due 09/22/2017 at 11:59pm MST
1. (1 point) Library/FortLewis/DiffEq/1-First-order/08-Existen
ce-uniqueness/KJ-2-1-16.pg
Consider the initial value problem
2ty0=8y,y(1) = −1.
(1) Find the value of the constant Cand the exponent rso
that y=Ctris the solution of this initial value problem.
y=help (formulas)
(2) Determine the largest interval of the form a<t<bon
which the existence and uniqueness theorem for first
order linear differential equations guarantees the exis-
tence of a unique solution.
help (inequalities)
(3) What is the actual interval of existence for the solution
(from part a)?
help (inequalities)
2. (1 point) Library/FortLewis/DiffEq/1-First-order/08-Existen
ce-uniqueness/KJ-2-1-13.pg
Consider the first order differential equation
y0+t
t2−9y=et
t−5.
For each of the initial conditions below, determine the largest
interval a<t<bon which the existence and uniqueness the-
orem for first order linear differential equations guarantees the
existence of a unique solution.
(1) y(−6) = −2.1.
help (inequalities)
(2) y(−1.5) = −3.14.
help (inequalities)
(3) y(0) = 0.
help (inequalities)
(4) y(4.5) = 6.4.
help (inequalities)
(5) y(6) = 2.6.
help (inequalities)
3. (1 point) Library/FortLewis/DiffEq/1-First-order/08-Existen
ce-uniqueness/Lebl-1-2-04.pg
Suppose y0=f(x,y) = xy
cos(x).
(1) ∂f
∂y=help (formulas)
(2) Since the function f(x,y)is
•Choose
•continuous
•not continuous
at the point (0,0), the partial derivative ∂f
∂y
•Choose
•exists
•does not exist
and is
•Choose
•continuous
•not continuous
at and near the point (0,0), the solution to y0=
f(x,y)
•Choose
•exists and is unique
•does not exist
near y(0) = 0
4. (1 point) Library/AlfredUniv/diffeq/ivp/existenceuniqueness
.pg
For the differential equations dy
dx =py2−49 does the exis-
tence/uniqueness theorem guarantee that there is a solution to
this equation through the point
? 1. (−4,51)?
? 2. (2,−7)?
? 3. (0,55)?
? 4. (−3,7)?
Generated by c
WeBWorK, http://webwork.maa.org, Mathematical Association of America
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