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For V(x, y) = ri –- yj do three things: (i) sketch the vector field, (ii) solve the differential equation (O) for the streamlines and sketch a few streamlines, and (iii) solve for the xy-equation directly. of the streamlines

For V(x, y) = ri –- yj do three things: (i) sketch the vector field, (ii) solve the differential equation (O) for the streamlines and sketch a few streamlines, and (iii) solve for the xy-equation directly. of the streamlines

Elements Of Electromagnetics
Elements Of Electromagnetics
7th Edition
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
ChapterMA: Math Assessment
Section: Chapter Questions
Problem 1.1MA
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Currently stuck on a StreamLine Problem, Need help to solve this. Thank you!

Let F(t) = x(t)i + y(t)j. Given a velocity vector field V : R? → R², the differential equation for the streamlines is (0) F(t) = V (r(t), y(t)). To solve (0) means to solve for x(t) and y(t) as functions of t. Often it is easier to solve for the ry-equation of the streamline by eliminating the parameter t via: dy ,dr dt' dt dy = y'(t)/r'(t). dæ For V (x, y) = xi – yj do three things: (i) sketch the vector field, (ii) solve the differential equation (O) for the streamlines and sketch a few streamlines, and (iii) solve for the ry-equation directly. of the streamlines For V (x, y) = (ri+ yj) //x² + y? complete items (i) and (iii) only.
Transcribed Image Text:Let F(t) = x(t)i + y(t)j. Given a velocity vector field V : R? → R², the differential equation for the streamlines is (0) F(t) = V (r(t), y(t)). To solve (0) means to solve for x(t) and y(t) as functions of t. Often it is easier to solve for the ry-equation of the streamline by eliminating the parameter t via: dy ,dr dt' dt dy = y'(t)/r'(t). dæ For V (x, y) = xi – yj do three things: (i) sketch the vector field, (ii) solve the differential equation (O) for the streamlines and sketch a few streamlines, and (iii) solve for the ry-equation directly. of the streamlines For V (x, y) = (ri+ yj) //x² + y? complete items (i) and (iii) only.
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