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Verify that the indicated function y = p(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, (у — х)у' %3D у — х + 18 %3 Since the left and right hand sides of the differential equation are equal when x + 6Vx + 4 is substituted for y, y = x + 6/x + 4 is a solution. Proceed as in Example 6, by considering p 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 (-4, 0) О (-8, 4) O (-8, -4] O (-∞, -4)

Verify that the indicated function y = p(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, (у — х)у' %3D у — х + 18 %3 Since the left and right hand sides of the differential equation are equal when x + 6Vx + 4 is substituted for y, y = x + 6/x + 4 is a solution. Proceed as in Example 6, by considering p 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 (-4, 0) О (-8, 4) O (-8, -4] O (-∞, -4)

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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Verify that the indicated function y = P(x) is an explicit solution of the given first-order differential equation. (у — х)у' %3 у - х+ 18; у %3Dх+ 6уx + 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 + 6/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.) Then by considering o as a solution of the differential equation, give at least one interval I of definition. O [-4, 4] O (-4, 0) О (-8, 4) О (-8, -4] O (-0, -4)
Transcribed Image Text:Verify that the indicated function y = P(x) is an explicit solution of the given first-order differential equation. (у — х)у' %3 у - х+ 18; у %3Dх+ 6уx + 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 + 6/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.) Then by considering o as a solution of the differential equation, give at least one interval I of definition. O [-4, 4] O (-4, 0) О (-8, 4) О (-8, -4] O (-0, -4)
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