dy dx 2y (x √y-1), y(0) = 1

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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Solve the following initial value problem by (possibly) using a suitable one
choice of substitution. Also determine the largest possible interval of validity. If able please provide some explanation with the taken steps, thank you in advance.

dy
dx
2y (x √y-1), y(0) = 1
Transcribed Image Text:dy dx 2y (x √y-1), y(0) = 1
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how do you decide the value of substitution? Are there certain steps or guide you can follow? Regarding the solution, how do you decide that v= 1/(sqrt(y)) is a good substitution?

 

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Follow-up Question

Is there perhaps an easier way to approach these questions? Im quite new to differential equation.

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