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jesuslovesu
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Homework Statement
(2x - y) + (2y-x) dy/dx = 0
y(1) = 3
Solve and determine where the solution is approximately valid.
Homework Equations
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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