Hyers–Ulam stability of Euler’s equation

We prove that Euler’s equation x 1 ∂ u ∂ x 1 + x 2 ∂ u ∂ x 2 + ⋯ + x n ∂ u ∂ x n = α u , characterising homogeneous functions, is stable in Hyers–Ulam sense if and only if α ∈ R ∖ { 0 } .