How Do You Solve (2x-y+1)dx+(x+y)dy=0 Using a Linear Transformation?

[asdf1]

Yes, you're right~
There's lots of different approaches to a question~
It's just that...
You guys are amazing!
I'd never of thought to come up with those ideas~
It makes me want to start jumping into mathematics books and brush up on my math~

 

[Hurkyl]

After homogenizing, the generic solution to the polar form looks like the product of these four terms to various powers: (if I haven't made a mistake)

(A + B tan θ + C tan² θ)
exp(arctan(D tan θ + E))
sec θ
exp(θ)

times some constant.

Sigh, not all that enlightening. Everything except the "some constant" depend on the coefficients in the original problem.