Solution Found!
M(x, y) dx + N(x, y) dy = 0 in the form You might start by
Chapter 2, Problem 31E(choose chapter or problem)
Explain why it is always possible to express any homogeneous differential equation M(x, y) dx + N(x, y) dy = 0 in the form
\(\frac{d y}{d x}=F\left(\frac{y}{x}\right)\).
You might start by proving that
\(M(x, y)=x^{\alpha} M(1, y / x)\) and \(N(x, y)=x^{\alpha} N(1, y / x)\)
Text Transcription:
dy/dx=F(y/x)
(M(x, y) = x^alpha M(1, y/x)
N(x, y) = x^alpha N(1, y/x)
Questions & Answers
QUESTION:
Explain why it is always possible to express any homogeneous differential equation M(x, y) dx + N(x, y) dy = 0 in the form
\(\frac{d y}{d x}=F\left(\frac{y}{x}\right)\).
You might start by proving that
\(M(x, y)=x^{\alpha} M(1, y / x)\) and \(N(x, y)=x^{\alpha} N(1, y / x)\)
Text Transcription:
dy/dx=F(y/x)
(M(x, y) = x^alpha M(1, y/x)
N(x, y) = x^alpha N(1, y/x)
ANSWER:Step 1 of 3
Given that
We have to explain why expression any homogeneous differential equation M(x, y) dx + N(x, y) dy = 0 in the form
is always possible.