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
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
Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter11: Differential Equations
Section11.CR: Chapter 11 Review
Problem 5CR
Question
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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