Discuss how to find an alternative two-parameter family of

Chapter 4, Problem 22E

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QUESTION:

Discuss how to find an alternative two-parameter family of solutions for the nonlinear differential equation \(y^{\prime \prime}=2 x\left(y^{\prime}\right)^{2}\) in Example 1. [Hint: Suppose that \(-c_{1}^{2}\) is used as the constant of integration instead of \(+c_{1}^{2}\).]

Text Transcription:

 y^prime\prime=2xy^prime^2

-c_1^2

Questions & Answers

QUESTION:

Discuss how to find an alternative two-parameter family of solutions for the nonlinear differential equation \(y^{\prime \prime}=2 x\left(y^{\prime}\right)^{2}\) in Example 1. [Hint: Suppose that \(-c_{1}^{2}\) is used as the constant of integration instead of \(+c_{1}^{2}\).]

Text Transcription:

 y^prime\prime=2xy^prime^2

-c_1^2

ANSWER:

Step 1 of 3

In this problem, we need to find the solution for the nonlinear differential equation              

     

 

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