Verify that the indicated function y = e(x) is an explicit solution of the given first-order differential equation. (у — х)у' %3D у — х+ 18; y = x + 6Vx + 4 When y = x + 6Vx + 4, y' = Thus, in terms of x, (y - x)y' = y - x + 18 = Since the left and right hand sides of the differential equation are equal when x + 6/x + 4 is substituted for y, y = x + 6Vx + 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.) Then by considering o as a solution of the differential equation, give at least one interval I of definition. O [-4, 4] O (-0, -4) О (-8, 4) (-4, c0)
Verify that the indicated function y = e(x) is an explicit solution of the given first-order differential equation. (у — х)у' %3D у — х+ 18; y = x + 6Vx + 4 When y = x + 6Vx + 4, y' = Thus, in terms of x, (y - x)y' = y - x + 18 = Since the left and right hand sides of the differential equation are equal when x + 6/x + 4 is substituted for y, y = x + 6Vx + 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.) Then by considering o as a solution of the differential equation, give at least one interval I of definition. O [-4, 4] O (-0, -4) О (-8, 4) (-4, c0)
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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![Verify that the indicated function y = g(x) is an explicit solution of the given first-order differential equation.
(у — х)у' %3D у — х+ 18;
y = x + 6Vx + 4
When y = x + 6Vx + 4,
y' =
Thus, in terms of x,
(y - x)y' =
y - x + 18 =
Since the left and right hand sides of the differential equation are equal when x + 6/x + 4 is substituted for y, y = x + 6Vx + 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.)
Then by considering o as a solution of the differential equation, give at least one interval I of definition.
O [-4, 4]
O (-0, -4)
О (-8, 4)
O (-4, 0)
О (-8, —4]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F737222ef-5c70-4907-93aa-2c2d7afd58f4%2F3e8c4734-5bee-4396-9d4d-143e61255a04%2Fssf29svx_processed.png&w=3840&q=75)
Transcribed Image Text:Verify that the indicated function y = g(x) is an explicit solution of the given first-order differential equation.
(у — х)у' %3D у — х+ 18;
y = x + 6Vx + 4
When y = x + 6Vx + 4,
y' =
Thus, in terms of x,
(y - x)y' =
y - x + 18 =
Since the left and right hand sides of the differential equation are equal when x + 6/x + 4 is substituted for y, y = x + 6Vx + 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.)
Then by considering o as a solution of the differential equation, give at least one interval I of definition.
O [-4, 4]
O (-0, -4)
О (-8, 4)
O (-4, 0)
О (-8, —4]
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