We find closed-form solution of the Euler equation for a chiral magnet in terms of a skyrmion or a meron depending on the relative strengths of magnetic anisotropy and magnetic field. We show that the relevant length scales for these solutions primarily depend on the strengths of Dzyaloshinskii-Moriya interaction through its ratios, respectively, with magnetic field and magnetic anisotropy. We thus unambiguously determine the parameter dependencies on the radius of the topological structures

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... ticularly of the skyrmions, showing an excellent agreement with experiments and first-principle studies. An anisotropic Dzyaloshinskii-Moriya interaction suitable for thin films made with C_nv symmetric materials is found to stabilize anti-skyrmion and anti-meron, which are prototypical for D_2d symmetric systems, depending on the degree of anisotropy. Based on these solutions, we obtain phase diagram by comparing the energies of various collinear and non-collinear competing phases.