Find an estimate for yo such that the solution to the initial value problem is guaranteed to satisfy the given inequality. 24. = xy + arctan(y), y(1) = yo > 1. y(3) < 5.

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
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Find an estimate for yo such that the solution to the initial value problem is guaranteed to satisfy
the given inequality.
24. = xy + arctan(y), y(1) = yo > 1.
dx
y(3) < 5.
25. = y? + xy+x + y, y(0) = yo > –1. y(.2) < 9.
(Show that z = –
-1 is a solution.)
26. = y? – x2 + 1, y(1) = yo > 1. y(1.1) < 3.
(Show that z = x is a solution. And y > x gives > 0, so y is increasing.)
Transcribed Image Text:Find an estimate for yo such that the solution to the initial value problem is guaranteed to satisfy the given inequality. 24. = xy + arctan(y), y(1) = yo > 1. dx y(3) < 5. 25. = y? + xy+x + y, y(0) = yo > –1. y(.2) < 9. (Show that z = – -1 is a solution.) 26. = y? – x2 + 1, y(1) = yo > 1. y(1.1) < 3. (Show that z = x is a solution. And y > x gives > 0, so y is increasing.)
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