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Let (t) satisfy the differential equation x"(t) + 14tx(t) = 0 for all t > 0. On the interval t > 0, define the functions ₁ (t) = x(t) and x₂ (t)=x"(t). Use the differential equation to express x2 (t) in terms of a(t). Note: Enter x (t) as x. Answer: ₂ (t) = = Enter the smallest pair of non-zero, integer values of A and B that satisfy the equation Ax₁(t) + Bx₂(t) = 0 if any. If there are no non-zero values enter 0 for each. Answer: A = B =

Let (t) satisfy the differential equation x"(t) + 14tx(t) = 0 for all t > 0. On the interval t > 0, define the functions ₁ (t) = x(t) and x₂ (t)=x"(t). Use the differential equation to express x2 (t) in terms of a(t). Note: Enter x (t) as x. Answer: ₂ (t) = = Enter the smallest pair of non-zero, integer values of A and B that satisfy the equation Ax₁(t) + Bx₂(t) = 0 if any. If there are no non-zero values enter 0 for each. Answer: A = B =

Advanced Engineering Mathematics
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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Let ä(t) satisfy the differential equation x"(t) + 14tx (t) = 0 for all t > 0. On the interval t > 0, define the functions x₁(t) = x(t) and x₂(t) = x"(t). Use the differential equation to express x₂ (t) in terms of x(t). Note: Enter x (t) as x. Answer: x₂(t) Enter the smallest pair of non-zero, integer values of A and B that satisfy the equation Ax₁ (t) + Bx₂(t) = 0 if any. If there are no non-zero values enter 0 for each. Answer: A = = 3 B = Therefore, for t > 0, the two functions must be: A. The same. B. The answers to the Navier-Stokes existence and smoothness problem. C. Linearly independent. D. Linearly dependent. E. Undefined. F. Discontinuous.
Transcribed Image Text:Let ä(t) satisfy the differential equation x"(t) + 14tx (t) = 0 for all t > 0. On the interval t > 0, define the functions x₁(t) = x(t) and x₂(t) = x"(t). Use the differential equation to express x₂ (t) in terms of x(t). Note: Enter x (t) as x. Answer: x₂(t) Enter the smallest pair of non-zero, integer values of A and B that satisfy the equation Ax₁ (t) + Bx₂(t) = 0 if any. If there are no non-zero values enter 0 for each. Answer: A = = 3 B = Therefore, for t > 0, the two functions must be: A. The same. B. The answers to the Navier-Stokes existence and smoothness problem. C. Linearly independent. D. Linearly dependent. E. Undefined. F. Discontinuous.
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