Explanation Given: d y d t = f ( t , y ) ; y 1 ( t ) = 4 , y 2 ( t ) = 2 and y 3 ( t ) = 0 for all t are solutions with initial condition y ( 0 ) = 1 And f ( t , y ) satisfies the hypotheses of Uniqueness Theorem in entire complex plane. Concept Used: The hypotheses of Uniqueness Theorem for the given differential equation of the form d y d t = f ( t , y ) ; y ( t 0 ) = y 0 states that, Suppose f ( t , y ) and ∂ f ∂ y are continuous functions in a rectangle of the form { ( t , y ) | a < t < b , c < y < d } in the ty-plane, if ( t 0 , y 0 ) is a point in the rectangle and if y 1 ( t ) and y 2 ( t ) be two solutions that solves given initial value problem then y 1 ( t ) = y 2 ( t ) f o r t 0 − ∈ < t < t 0 + ∈ , where ∈ some positive number

4th Edition

ISBN: 9780495561989

Author: Paul Blanchard, Robert L. Devaney, Glen R. Hall

Publisher: Cengage Learning

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Chapter 1.5, Problem 2E

To determine

The behavior of the solutions to the differential equation dydt=f(t,y);

y1(t)=4 ,y2(t)=2 and y3(t)=0 for all t are solutions with initial condition y(0)=1 by using uniqueness theorem.

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Chapter 1.5, Problem 1E

Chapter 1.5, Problem 3E

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The behavior of the solutions to the differential equation d y d t = f ( t , y ) ; y 1 ( t ) = 4 , y 2 ( t ) = 2 and y 3 ( t ) = 0 for all t are solutions with initial condition y ( 0 ) = 1 by using uniqueness theorem.

Solution Summary: The author analyzes the behavior of the solutions to the differential equation dy-dt=f(t,y) and the hypotheses of Uniqueness theorem in the entire complex plane

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The behavior of the solutions to the differential equation dydt=f(t,y);

y1(t)=4 ,y2(t)=2 and y3(t)=0 for all t are solutions with initial condition y(0)=1 by using uniqueness theorem.

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Chapter 1 Solutions

The behavior of the solutions to the differential equation d y d t = f ( t , y ) ; y 1 ( t ) = 4 , y 2 ( t ) = 2 and y 3 ( t ) = 0 for all t are solutions with initial condition y ( 0 ) = 1 by using uniqueness theorem.

Solution Summary: The author analyzes the behavior of the solutions to the differential equation dy-dt=f(t,y) and the hypotheses of Uniqueness theorem in the entire complex plane

Concept explainers

Videos

The behavior of the solutions to the differential equation dydt=f(t,y); y1(t)=4 ,y2(t)=2 and y3(t)=0 for all t are solutions with initial condition y(0)=1 by using uniqueness theorem.

Want to see the full answer?

Chapter 1 Solutions

The behavior of the solutions to the differential equation dydt=f(t,y);

y1(t)=4 ,y2(t)=2 and y3(t)=0 for all t are solutions with initial condition y(0)=1 by using uniqueness theorem.