1. Consider the equation a" – 2x(1+ a²) = 0 with initial conditions æ(0) = 0, a'(0) = 1. (a) Write as a system of first order equations in the standard way. (b) What does Theorem 7.1.1 say about existence and uniqueness of solutions? (c) Show that a = tan(t) is a solution by confirming that it satisfies the differential equation and initial condition.
1. Consider the equation a" – 2x(1+ a²) = 0 with initial conditions æ(0) = 0, a'(0) = 1. (a) Write as a system of first order equations in the standard way. (b) What does Theorem 7.1.1 say about existence and uniqueness of solutions? (c) Show that a = tan(t) is a solution by confirming that it satisfies the differential equation and initial condition.
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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![1. Consider the equation a" – 2x(1+ a²) = 0 with initial conditions æ(0) = 0, a'(0) = 1.
(a) Write as a system of first order equations in the standard way.
(b) What does Theorem 7.1.1 say about existence and uniqueness of solutions?
(c) Show that a = tan(t) is a solution by confirming that it satisfies the differential equation
and initial condition.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F793eca03-fdd3-46eb-bc34-64c6ba68c408%2F18149f1d-30d8-49ae-90e7-b9cd08b8992f%2Fhec2q3m.png&w=3840&q=75)
Transcribed Image Text:1. Consider the equation a" – 2x(1+ a²) = 0 with initial conditions æ(0) = 0, a'(0) = 1.
(a) Write as a system of first order equations in the standard way.
(b) What does Theorem 7.1.1 say about existence and uniqueness of solutions?
(c) Show that a = tan(t) is a solution by confirming that it satisfies the differential equation
and initial condition.
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