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The normal form (5) of an nth-order differential equation
Chapter 1, Problem 53E(choose chapter or problem)
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