I have the following easy ODE $$y''=y'+x$$ I am required to compute the Lipschitz constant of the r.h.s. which is (after reducing to first order):$$f([y,y'],x)=[y',y'+x]^t$$
I thought I could just compute the Jacobian, which is
$$J_f = \begin{bmatrix} 0 & 1 \\ 0 & 1 \end{bmatrix} $$
and since $||J_f||_{\inf}=1$ I'd say that the Lipschitz constant $L =1$. Is this the right way?