Solving (x - 2y - 3)dx + (2x + y - 1)dy = 0

00:00 Intro
01:00 Introducing X, Y, h, & k
04:02 The Simplified Problem
05:20 Getting dY/dX
06:07 Introducing v(x) and Simplifying
11:07 Integrating
13:56 Final Answer (Almost)
14:13 Forgetting to multiply tan by 2
14:14 Final Answer (Almost)
16:08 Remembering the missing 2
16:23 Final Simplified Answer
17:25 Outro

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Note
If any mistakes are made please let me know in the comments down below, I'm only human and will endeavour to be correct as much as I can!

[davidblauyoutube]

The form of the solution strongly suggests the use of polar coordinates (X, Y) = (r cos θ, r sin θ). This change of coordinates turns the solution into r + 2θ = c, a pretty family of spirals. In (x, y) coordinates these spirals are translated one unit to the right and one unit down in the plane.

[holyshit]

Here form of the equation sugests us exact equaton
Fortunately (x - 2y - 3) and (2x + y -1) satisfies Cauchy-Riemann equation so integrating factor is quite easy to find
We can also reduce this equation to homogeneous

[andrea-mjce]

I don't understand the problem, should we find a function of X and y?

[thomasblackwell]

You could have used better notation; it is really confusing!