Prompt Title: Integral Curves Definition

Created 11 months ago
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You are correct! I apologize for the mistake in my previous response. The correct integration of dx/(-x+t) is:

∫dx/(-x+t) = - ln|-x+t| + C

Substituting this into our differential equation, we have:

-ln|-x+t| = ln|y-t| + C

Simplifying, we get:

|-x+t| = e^C|y-t|

Squaring both sides, we get:

(x-t)^2 = e^(2C)(y-t)^2

This is the equation for the streamlines of the flow. It represents a family of ellipses centered at (t, t) with major axis along the x-axis and minor axis along the y-axis. The value of the constant e^C determines the shape and size of the ellipse, with larger values of e^C corresponding to larger ellipses.

Again, I apologize for the error in my previous response. Thank you for bringing it to my attention.

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Allan Erissat
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Created 11 months ago

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