Spring 2019
2.4 Linear vs Nonlinear
1. (1 point) For the differential equations dxdy =py2−9 does the
existence/uniqueness theorem guarantee that there is a solu-
3. (1 point) Consider the first order differential equation
0 t et
y + y = . t2−25 t −6
For each of the initial conditions below, determine the
largest interval a < t < b on which the existence and
uniqueness theorem for first order linear differential
equations guarantees the existence of a unique solution.
tion to this equation through the point
? 1. (−6,12)?
? 2. (−4,18)?
Assignment Section 2.4 Linear vs Nonlinear due 01/17/2019 at 11:59pm MST
? 3. (−5,3)?
? 4. (−1,−3)?
Answer(s) submitted:
•true
•true
•false
•false
(correct)
Correct Answers:
•TRUE
•TRUE
•FALSE
•FALSE
2. (1 point) Consider the initial value problem
2ty0 = 6y, y(1)=−1.
(1) y(−6)= 1.7.
(2) y(−3.5)= 6.4.
(3) y(0)= 0.
(4) y(5.5)=−2.1.
(5) y(9)= 1.7.
help (inequalities)
help (inequalities)
help (inequalities)
help (inequalities)
help (inequalities)
0
(1) Find the value of the constant C and the exponent r so Answer(s) submitted: that y
=Ctr is the solution of this initial value problem. • -INF<t<-5 y =
help (formulas) • -5<t<5
•-
5<t<5 (2) Determine the largest interval of the form a < t < b on • 5<t<6 •
6<t<INF which the existence and uniqueness theorem for first order linear
differential equations guarantees the exis- (correct) tence of a unique
solution. Correct Answers:
help (inequalities) • t < -5
•-
5 < t < 5
(3) What is the actual interval of existence for the solution • -5 < t < 5
•5 < t < 6
(from part a)?
•6 < t help (inequalities)
Answer(s) submitted: 4. (1 point) Suppose y = f(x,y)= .
cos(x)
•-1tˆ3
•0<t<INF ∂f
(1) =help (formulas)
•-INF<t<INF ∂y
(correct) (2) Since the function f(x,y) is
Correct Answers:
•Choose
•-1*tˆ3 •continuous
•0 < t
•not continuous
•-infinity < t < infinity at the point (0,0), the partial derivative ∂∂yf
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:
•(x)/(cos(x))
•continuous
•exists
•continuous
•exists and is unique
(correct)
Correct Answers:
•x*cos(x)/([cos(x)]ˆ2)
•continuous
•exists
•continuous
