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Separation of Variables kample 2: Find the particular solution of 2xyy' = 1 + y? when x = 2 & y plution: eparating the variables, ry = 1+ y? dx = 0 2ydy ку %3D - dx 1+y? ( 2ydy 1+y2 dx - In(1 + y2) – In x = In c (1+y' In (**) = In c 1+y2 = C This is the general solution.

Separation of Variables kample 2: Find the particular solution of 2xyy' = 1 + y? when x = 2 & y plution: eparating the variables, ry = 1+ y? dx = 0 2ydy ку %3D - dx 1+y? ( 2ydy 1+y2 dx - In(1 + y2) – In x = In c (1+y' In (**) = In c 1+y2 = C This is the general solution.

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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Separation of Variables Example 2: Find the particular solution of 2xyy' = 1 + y? when x = 2 & y = 3 Solution: Separating the variables, dy 2ydy dx 2xy = 1+ y2 → 1+y2 %| - dx ( 2ydy dx S = 5 0 - %3D 1+y2 In(1 + y2) – Inx = In c - In () = In e 1+y2 = C This is the general solution.
Transcribed Image Text:Separation of Variables Example 2: Find the particular solution of 2xyy' = 1 + y? when x = 2 & y = 3 Solution: Separating the variables, dy 2ydy dx 2xy = 1+ y2 → 1+y2 %| - dx ( 2ydy dx S = 5 0 - %3D 1+y2 In(1 + y2) – Inx = In c - In () = In e 1+y2 = C This is the general solution.
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