Because the circle is tangent to the Y axis, the distance from the center of the circle to the Y axis is the radius r=lal.

Because the center of the circle is 2x-y=0, let the distance from the center of the circle C(a, 2a) to the straight line y=x+ 1 be d=la- 1l/√2.

If the straight line passing through the center of the circle is perpendicular to the straight line y=x+ 1, let the intersection point be b, and the half chord length of the circle cut by the straight line y=x+ 1 is 1.

According to the Pythagorean theorem d∧2+ 1∧2=r∧2(r is the radius), the solution is a=-3 or 1, and then C(-3, -6) or (1, 2).

Then the equation of the circle is (x+3)∧2+(y+6)∧2=9 or (x- 1)∧2+(y-2)∧2= 1.