1. The problem statement, all variables and given/known data Hi. I am trying to solve a problem on renormalisation group flow and have come across the following coupled equations that I need to solve: Λ ∂g/∂Λ = b.m Λ ∂m/∂Λ = -2.m + a.g Where a and b are just constants. I need to find g(Λ) and m(Λ). 2. Relevant equations I thought this could perhaps be solved by turning it into a matrix equation and then diagonalising and expressing g(Λ) and m(Λ) as sums of eigenvectors. 3. The attempt at a solution First I found the eigenvalues of the matrix to give: λ+ = -1 + √(1+ab) λ- = -1 - √(1+ab) And then I found the eigenvectors of the operator Λ ∂/∂Λ : ν+(Λ) = (Λ/μ)λ+ ν+(μ) Where μ is just some integration constant. A similar expression holds for ν- I then decomposed: g(Λ) = α ν+ + β ν- m(Λ) = γ ν+ + δ ν- But I don't really know where to go from here? Any help would be greatly appreciated!