The normal form (5) of an nth-order differential equation

Chapter 1, Problem 53E

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QUESTION:

The normal form (5) of an nth-order differential equation is equivalent to (4) whenever both forms have exactly the same solutions. Make up a first-order differential equation for which \(F\left(x, y, y^{\prime}\right)=0\) is not equivalent to the normal form dy/dx = f(x, y).

Text Transcription:

F(x, y, y^prime) = 0

Questions & Answers

QUESTION:

The normal form (5) of an nth-order differential equation is equivalent to (4) whenever both forms have exactly the same solutions. Make up a first-order differential equation for which \(F\left(x, y, y^{\prime}\right)=0\) is not equivalent to the normal form dy/dx = f(x, y).

Text Transcription:

F(x, y, y^prime) = 0

ANSWER:

Step 1 of 4

Consider the differential condition yy'- xy =0, and the relating normal frame is

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