(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

(2x - y) + (2y-x) dy/dx = 0

y(1) = 3

Solve and determine where the solution is approximately valid.

2. Relevant equations

3. The attempt at a solution

Ux = 2x - y

Uy = 2y - x

U = x^2 - yx + h(y)

Uy = 2y -x = -x + h'(y)

h'(y) = 2y

h(y) = y^2

x^2 - yx + y^2 = c

1 - 3 + 3^2 = c = 7

I'm not really sure where to go from here,

x^2 - yx + y^2 = 7

However, the answer is quite a bit different:

y = x + sqrt( 28 - 3x^2)/2 and I can't quite see the step toward that. (x-y)^2 = 7-xy but I still can't seem to solve for y

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# Homework Help: Differential Equation Exact Solution

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