Assignment Section...2.4_Linear_vs_Nonlinear due 09/01/2021 at 11:59pm MST
Problem 1. (1 point)
For the differential equation * = J y2 -81 does the exis
tence/uniqueness theorem guarantee that there is a solution to
this equation through the point
[2]1. (-4, 87)?
[2]2. (-8, 83)?
[2]3. (-3, -9)?
[2]4. (-7,9)?
Answer(s) submitted:
•true
•true
•false
•false
(correct)
Problem 2. (1 point)
Consider the initial value problem
2ty' =4y, y(-l) = l.
(1) Find the value of the constant C and the exponent r so that
y =Ctr is the solution of this initial value problem.
y = ____ help (formulas)
(2) Determine the largest interval of the form a < t < b on
which the existence and uniqueness theorem for first or
der linear differential equations guarantees the existence
of a unique solution.
______ help (inequalities)
(3) What is the actual interval of existence for the solution
(from part a)?
_____ help (inequalities)
Answer(s) submitted:
• t A (2)
•-inf<t<O
•t<inf
(correct)
Problem 3. (1 point)
Consider the first order differential equation
For each of the initial conditions below, determine the largest in
terval a < t < b on which the existence and uniqueness theorem
for first order linear differential equations guarantees the existence
of a unique solution.
(1) y(-4) = -5.5.
______ help (inequalities)
(2) y(-0.5) = -5.5.
______ help (inequalities)
(3) y(O) = 0.
______ help (inequalities)
(4) y(4.5) = -4.
______ help (inequalities)
(5) y(9) = 2.6.
______ help (inequalities)
Answer(s) submitted:
•-inf<t<-3
•-3<t<3
•-3<t<3
•3<t<5
•S<t<inf
(correct)
Problem
4.
(1
point)
Suppose
y’
=
f(x,y)
=
eats)
.
(1)
of
=
help
(formulas)
y
(2)
Since
the
function
f(x,y)
is
¢
Choose
*
continuous
*
not
continuous
at
the
point
(0,0),
the
partial
derivative
“
¢
Choose
°
exists
¢
does
not
exist
Generated
by
©WeB
Work,
http://webwork.maa.org,
Mathematical
Association
of
America
and
is
¢
Choose
*
continuous
*
not
continuous
at
and
near
the
point
(0,0),
the
solution
to
y’
=
f(x,y)
¢
Choose
*
exists
and
is
unique
¢
does
not
exist
near
y(0)
=0
Answer(s)
submitted:
(correct)
(x/
(cosx)
)
continuous
exists
continuous
exists and
is
unique
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