That's a good strategy, but you should have other tools for non-linear problems in your toolbox too. I mostly want to push back against the idea that non-linea

That's a good strategy, but you should have other tools for non-linear problems in your toolbox too. I mostly want to push back against the idea that non-linear means unsolvable. My example transformed the problem to a linear one, but that's not the only possibility. Look at my other link for many other examples. Autonomous ordinary differential equations are one possible class of ODEs which don't need to be transformed to a linear system to be solved: https://en.wikipedia.org/wiki/Autonomous_differential_equation https://en.wikipedia.org/wiki/Autonomous_differential_equati... You can often solve a non-linear autonomous ODE by direct integration.