Verify that the indicated function y = (x) is an explicit solution of the given first-order differential equation. (y - x)y' = y - x + 2; y = x + 2√x +4 When y = x + 2√x + 4, y' = x. Thus, in terms of x, (y - x)y' = y-x + 2 = Since the left and right hand sides of the differential equation are equal when x + 2√x + 4 is substituted for y, y = x + 2√x + 4 is a solution. Proceed as in Example 6, by considering o simply as a function and give its domain. (Enter your answer using interval notation.)

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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Verify that the indicated function y = (x) is an explicit solution of the given first-order differential equation.
(y - x)y' = y - x + 2;
y = x + 2√x +4
When y = x + 2√x + 4,
y' =
x.
Thus, in terms of x,
(y - x)y' =
y-x + 2 =
Since the left and right hand sides of the differential equation are equal when x + 2√x + 4 is substituted for y, y = x + 2√x + 4 is a solution.
Proceed as in Example 6, by considering o simply as a function and give its domain. (Enter your answer using interval notation.)
Transcribed Image Text:Verify that the indicated function y = (x) is an explicit solution of the given first-order differential equation. (y - x)y' = y - x + 2; y = x + 2√x +4 When y = x + 2√x + 4, y' = x. Thus, in terms of x, (y - x)y' = y-x + 2 = Since the left and right hand sides of the differential equation are equal when x + 2√x + 4 is substituted for y, y = x + 2√x + 4 is a solution. Proceed as in Example 6, by considering o simply as a function and give its domain. (Enter your answer using interval notation.)
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