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Example 1: Eliminate the arbitrary constant of xy – 2 = cy. Solution: Let xy? - 2 - cy be Equation (1). Substituting c = to Equation (2). we get xy2-2 dy Differentiating the equation, we get x(2ydy) + y'dx - ( x(2ydy) + y-dx = cảy as Equation (2). And then simplity to get Note that from Equation (1), we have ydx + (xy? + 2)dy - 0 or ху? - 2 dy ya y dx' xy + 2

Example 1: Eliminate the arbitrary constant of xy – 2 = cy. Solution: Let xy? - 2 - cy be Equation (1). Substituting c = to Equation (2). we get xy2-2 dy Differentiating the equation, we get x(2ydy) + y'dx - ( x(2ydy) + y-dx = cảy as Equation (2). And then simplity to get Note that from Equation (1), we have ydx + (xy? + 2)dy - 0 or ху? - 2 dy ya y dx' xy + 2

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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Example 1: Eliminate the arbitrary constant of xy – 2 = cy. Solution: Let xy? - 2 - cy be Equation (1). Substituting c = to Equation (2). we get xy2-2 dy Differentiating the equation, we get x(2ydy) + y'dx - ( x(2ydy) + y-dx = cảy as Equation (2). And then simplity to get Note that from Equation (1), we have ydx + (xy? + 2)dy - 0 or ху? - 2 dy ya y dx' xy + 2
Transcribed Image Text:Example 1: Eliminate the arbitrary constant of xy – 2 = cy. Solution: Let xy? - 2 - cy be Equation (1). Substituting c = to Equation (2). we get xy2-2 dy Differentiating the equation, we get x(2ydy) + y'dx - ( x(2ydy) + y-dx = cảy as Equation (2). And then simplity to get Note that from Equation (1), we have ydx + (xy? + 2)dy - 0 or ху? - 2 dy ya y dx' xy + 2
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