Determine whether a conclusion can be drawn about the existence of uniqueness of a solution of the differential equation {z" +7tz' + 4z = cost, given that z(0) = 4 and z'(0) = 4. If a conclusion can be drawn, discuss it. If a conclusion cannot be drawn, explain why. Select the correct choice below and fill in any answer boxes to complete your choice. O A. No conclusion can be drawn because the conditions z(0) = 4 and z'(0) = 4 do not provide enough information to determine all constants of integration. OB. A solution is guaranteed only at the point to = because the functions p(t)=,q(t) = simultaneously defined at that point. OC. No conclusion can be drawn because the functions p(t) = continuous on any interval that contains the point t₁ =- q(t) = and g(t) = O D. A solution is guaranteed on the interval because it contains the point to = p(t)=,q(t)=, and g(t)=[ are simultaneously continuous on the interval. and g(t) = are are not simultaneously and the functions
Determine whether a conclusion can be drawn about the existence of uniqueness of a solution of the differential equation {z" +7tz' + 4z = cost, given that z(0) = 4 and z'(0) = 4. If a conclusion can be drawn, discuss it. If a conclusion cannot be drawn, explain why. Select the correct choice below and fill in any answer boxes to complete your choice. O A. No conclusion can be drawn because the conditions z(0) = 4 and z'(0) = 4 do not provide enough information to determine all constants of integration. OB. A solution is guaranteed only at the point to = because the functions p(t)=,q(t) = simultaneously defined at that point. OC. No conclusion can be drawn because the functions p(t) = continuous on any interval that contains the point t₁ =- q(t) = and g(t) = O D. A solution is guaranteed on the interval because it contains the point to = p(t)=,q(t)=, and g(t)=[ are simultaneously continuous on the interval. and g(t) = are are not simultaneously and the functions
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:Determine whether a conclusion can be drawn about the existence of uniqueness of a solution of the differential equation
tz" +7tz' + 4z = cost, given that z(0) = 4 and z'(0) = 4. If a conclusion can be drawn, discuss it. If a conclusion cannot
be drawn, explain why.
Select the correct choice below and fill in any answer boxes to complete your choice.
O A. No conclusion can be drawn because the conditions z(0) = 4 and z'(0) = 4 do not provide enough information to
determine all constants of integration.
OB. A solution is guaranteed only at the point to = because the functions p(t) =
simultaneously defined at that point.
OC. No conclusion can be drawn because the functions p(t) =
continuous on any interval that contains the point to =
O D. A solution is guaranteed on the interval
p(t)=,q(t) = and g(t) =
q(t) =
and g(t) =
q(t) =
because it contains the point to =
are simultaneously continuous on the interval.
and g(t) = are
are not simultaneously
and the functions
Transcribed Image Text:Discuss the existence and uniqueness of a solution to the differential equation (6+t²) y'" +ty' - y = tant that satisfies
the initial conditions y(3)=Yo, y'(3)=Y₁ where Yo and Y₁ are real constants.
Select the correct choice below and fill in any answer boxes to complete your choice.
OA. A solution is guaranteed only at the point to =
simultaneously defined at that point.
O B. A solution is guaranteed on the interval
p(t)=₁,q(t) = and g(t) =
because the functions p(t) =
q(t) =
because it contains the point to
are simultaneously continuous on the interval.
OC. A solution is guaranteed on the interval <t< because it contains the point to
p(t) = =,q(t) = and g(t) = are equal on the interval.
and g(t) = are
and the functions
and the functions
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