Convert $\| \cdot \|_2 = 0$ to DCP form

Question

I am interested in writing the following equality constraint

$$\|(x+2y, x-y)\|_2 = 0$$

in the Disciplined Convex Programming (DCP) form. I don't know how to convert the operator == to satisfy DCP form which presents at above website. I have tested and got that

• affine_func == affine_func is satisfied

• affine_func == contant is satisfied

• contant == affine_func is satisfied

• constant == constant is satisfied

but when i use convex or concave function then the expression can not be satisfied. Can anyone please help me?