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This question is probably very elementary but I don't know how to tackle the conversely part of the following result. Let $M(x,y)$ and $N(x,y)$ be two differentiable and homogeneous functions of the ...

Setup I have recently come across an ODE of the form $$ 0 = \dot{A}(t)^TG(t) + A(t)^T\dot{G}(t) + C(t) + \lambda B(t)^TA(t)G(t) + \frac{\lambda}{2} (D(t)A(t)G(t))(D(t)A(t)G(t))^T\bar{1}, $$ where $\...