The previous ODE is an example of a quasi-homogeneous differential equation. An ODE y = f(x, y) is quasi-homogeneous if for any 0 and some a, b #0, ƒ(Aªx, Xy) = X-ª f(x, y). Prove that if an ODE is homogeneous, then it is quasi-homogeneous. To solve a quasi-homogeneous ODE, we need the substitution y = it into a separable ODE. Prove this fact. vrb/a to turn

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Question
The previous ODE is an example of a quasi-homogeneous differential equation.
An ODE y = f(x, y) is quasi-homogeneous if for any 0 and some a, b #0,
ƒ(Aªx, Xy) = X-ª f(x, y).
Prove that if an ODE is homogeneous, then it is quasi-homogeneous.
To solve a quasi-homogeneous ODE, we need the substitution y =
it into a separable ODE. Prove this fact.
vrb/a to turn
Transcribed Image Text:The previous ODE is an example of a quasi-homogeneous differential equation. An ODE y = f(x, y) is quasi-homogeneous if for any 0 and some a, b #0, ƒ(Aªx, Xy) = X-ª f(x, y). Prove that if an ODE is homogeneous, then it is quasi-homogeneous. To solve a quasi-homogeneous ODE, we need the substitution y = it into a separable ODE. Prove this fact. vrb/a to turn
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