Let F(t) = x(t)i+ y(t)j. Given a velocity vector field V : R² → R², the differential equation for the streamlines is (0) " (t) = V (x(t), y(t)). To solve (0) means to solve for #(t) and y(t) as functions of t. Often it is easier to solve for the ay-equation of the streamline by eliminating the parameter t via: dy dy ,dx = y'(t)/a' (t). dr dt' dt For V (r, y) = xi – yj do three things: (i) sketch the vector field, (ii) solve the differential equation (0) for the streamlines and sketch a few streamlines, and (iii) solve for the xy-equation directly. of the streamlines

Let F(t) = x(t)i+ y(t)j. Given a velocity vector field V : R² → R², the differential equation for the streamlines is (0) " (t) = V (x(t), y(t)). To solve (0) means to solve for #(t) and y(t) as functions of t. Often it is easier to solve for the ay-equation of the streamline by eliminating the parameter t via: dy dy ,dx = y'(t)/a' (t). dr dt' dt For V (r, y) = xi – yj do three things: (i) sketch the vector field, (ii) solve the differential equation (0) for the streamlines and sketch a few streamlines, and (iii) solve for the xy-equation directly. of the streamlines

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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