Consider the following differential equation, (x - 81)y" + sin(4x)y' = In(1 + 6x²) cos(x²)y. What is the largest interval for which Theorem 2 implies a unique solution to the differential equation with the following conditions? If your interval is (a, b), then enter the values of a and b (in that order) into the answer box, separated with a comma. (Use infinity for ∞, if needed.) If Theorem 2 does not provide an interval, then enter DNE , DNE (а) у(1) %3D 2, у (1) (b) у(-1) %3D 2, у'(-2) 3 3 = 2. (c) y(-18) = 2, y'(-18) = 4
Consider the following differential equation, (x - 81)y" + sin(4x)y' = In(1 + 6x²) cos(x²)y. What is the largest interval for which Theorem 2 implies a unique solution to the differential equation with the following conditions? If your interval is (a, b), then enter the values of a and b (in that order) into the answer box, separated with a comma. (Use infinity for ∞, if needed.) If Theorem 2 does not provide an interval, then enter DNE , DNE (а) у(1) %3D 2, у (1) (b) у(-1) %3D 2, у'(-2) 3 3 = 2. (c) y(-18) = 2, y'(-18) = 4
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:Consider the following differential equation,
(x - 81) y" + sin(4x)y' = ln(1 + 6x²) cos(x²)y.
What is the largest interval for which Theorem 2 implies a unique solution to the differential equation with the
following conditions?
If your interval is (a, b), then enter the values of a and b (in that order) into the answer box, separated with a
comma. (Use infinity for ∞, if needed.)
If Theorem 2 does not provide an interval, then enter DNE,
DNE
(а) у(1) %3D 2, у'(1) 3 2.
(b) у(-1) 3D 2, у'-2) — 3
(c) y(-18) = 2, y'(-18) = 4
%3D
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