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Consider the ODE dx /+/2y1/2 + y x1/2y/2x Let g(x,y) be that monstrosity on the right-hand side. Show that g(Ax‚àªy) = \*¯€ g(x, y). Show that the substitution y = vx/e reduces the original ODE to a separable one (you do not need to solve it).

Consider the ODE dx /+/2y1/2 + y x1/2y/2x Let g(x,y) be that monstrosity on the right-hand side. Show that g(Ax‚àªy) = \*¯€ g(x, y). Show that the substitution y = vx/e reduces the original ODE to a separable one (you do not need to solve it).

Calculus For The Life Sciences
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.
Chapter9: Multivariable Calculus
Section9.2: Partial Derivatives
Problem 28E
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Consider the ODE dx /+/2y1/2 + y x1/2y/2x Let g(x,y) be that monstrosity on the right-hand side. Show that g(Ax‚àªy) = \*¯€ g(x, y). Show that the substitution y = vx/e reduces the original ODE to a separable one (you do not need to solve it).
Transcribed Image Text:Consider the ODE dx /+/2y1/2 + y x1/2y/2x Let g(x,y) be that monstrosity on the right-hand side. Show that g(Ax‚àªy) = \*¯€ g(x, y). Show that the substitution y = vx/e reduces the original ODE to a separable one (you do not need to solve it).
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