Austin Cholley Jones MAT 275 ONLINE B Spring 2021
Assignment Section 2.4 Linear vs Nonlinear due 03/17/2021 at 11:59pm MST
1. (1 point) For the differential equation dy
dx =py2−49 does
the existence/uniqueness theorem guarantee that there is a solu-
tion to this equation through the point
? 1. (−3,52)?
? 2. (2,−7)?
? 3. (1,58)?
? 4. (0,7)?
Answer(s) submitted:
•true
•false
•true
•false
(correct)
Correct Answers:
•TRUE
•FALSE
•TRUE
•FALSE
2. (1 point) 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)
Answer(s) submitted:
•tˆ(4)
•x_(0)-delta2<x<x_(0)+delta2
•(-inf,0)U(0,inf)
(score 0.333333333333333)
Correct Answers:
•1*tˆ4
•t<0
•-infinity < t < infinity
3. (1 point) Consider the first order differential equation
y0+t
t2−25 y=et
t−6.
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) = 6.4.
help (inequalities)
(2) y(−1.5) = −4.
help (inequalities)
(3) y(0) = 0.
help (inequalities)
(4) y(5.5) = −4.
help (inequalities)
(5) y(9) = 2.6.
help (inequalities)
Answer(s) submitted:
•
•
•
•
•
(incorrect)
Correct Answers:
•t < -5
•-5<t<5
•-5<t<5
•5<t<6
•6<t
4. (1 point) 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
1
• 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
Answer(s) submitted:
•
•
•
•
•
(incorrect)
Correct Answers:
•x*cos(x)/([cos(x)]ˆ2)
•continuous
•exists
•continuous
•exists and is unique
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