A function F (x,y) is said to be homogeneous of degree n if F(yx, yy) = y"F(x,y) Determine which of the following functions are homogeneous and the corresponding degree. If the differential equation contains homogeneous functions, find its solution. 8. [2xsin² + 2xtan-ycos-ysec²2]dx + [xcos ² + xsec²²]dy = 0

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
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A function F (x,y) is said to be homogeneous of degree n if F(yx, yy) = y¹ F(x,y)
Determine which of the following functions are homogeneous and the
corresponding degree. If the differential equation contains homogeneous
functions, find its solution.
8. [2xsin + 2xtanycos-ysec²dx + [xcos² + xsec²dy = 0
Transcribed Image Text:A function F (x,y) is said to be homogeneous of degree n if F(yx, yy) = y¹ F(x,y) Determine which of the following functions are homogeneous and the corresponding degree. If the differential equation contains homogeneous functions, find its solution. 8. [2xsin + 2xtanycos-ysec²dx + [xcos² + xsec²dy = 0
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