In 3 –6, is a one-parameter family of solutions of the

Chapter 1, Problem 3E

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QUESTION:

In Problems 3–6, \(y=1 /\left(x^{2}+c\right)\) is a one-parameter family of solutions of the first-order DE \(y^{\prime}+2 x y^{2}=0\). Find a solution of the first-order IVP consisting of this differential equation and the given initial condition. Give the largest interval I over which the solution is defined

\(y(2)=\frac{1}{3}\)

Text Transcription:

y = 1/(x^2 + c)

y^prime + 2xy^2 = 0

y(2)=1/3

Questions & Answers

QUESTION:

In Problems 3–6, \(y=1 /\left(x^{2}+c\right)\) is a one-parameter family of solutions of the first-order DE \(y^{\prime}+2 x y^{2}=0\). Find a solution of the first-order IVP consisting of this differential equation and the given initial condition. Give the largest interval I over which the solution is defined

\(y(2)=\frac{1}{3}\)

Text Transcription:

y = 1/(x^2 + c)

y^prime + 2xy^2 = 0

y(2)=1/3

ANSWER:

Step 1 of 3

In this problem we need to find the particular solution of the differential equation for the given initial condition.

 

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