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Consider the initial value problem dy/dx = 2x/(y − 1), y(0) = y0. a. Solve this initial value problem for y0 ∈ R\{1}. Always give as large as possible interval at which the solution exists. b. Describe the set of solutions geometrically and make a sketch of the total pattern of solutions. What happens if y0  → 1? please if able provide some explanation with the steps, thank you in adavance.

Consider the initial value problem dy/dx = 2x/(y − 1), y(0) = y0. a. Solve this initial value problem for y0 ∈ R\{1}. Always give as large as possible interval at which the solution exists. b. Describe the set of solutions geometrically and make a sketch of the total pattern of solutions. What happens if y0  → 1? please if able provide some explanation with the steps, thank you in adavance.

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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Consider the initial value problem
dy/dx = 2x/(y − 1), y(0) = y0.
a. Solve this initial value problem for y0 ∈ R\{1}. Always give as large as possible
interval at which the solution exists.
b. Describe the set of solutions geometrically and make a sketch of the total
pattern of solutions. What happens if y0  → 1?

please if able provide some explanation with the steps, thank you in adavance.

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Im kind of confused with the integration of (y-1), can it also be ((y2)/2)-y?

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