2nd order diff eqn

After we had the back and forth I went back to doing M4 and M5 and a lot of the Damped/Forced Harmonic equations and the Vector differentials you set up are actually disguised 1st orders, so I figured that if it did come up, it'd be nice to solve a potentially easier equation and save myself time for the rest of the paper.

Anyway, glad to see it works, I shall use it in future .

It may be worthwhile to go back and solve the ODE as a 2nd order and compare the time/effort it demanded. Who knows? You may be more comfortable with 2nd order differential equations.

I'd say that although I'm obviously currently more comfortable with 2nd ODEs, I timed myself roughly and doing it the regular 2nd ODE way took a good 2-3 more minutes just because there's more steps and more calculations etc, and, potentially, more ways to make a mistake.

Plus, sometimes, realising what the PI is isn't always obvious (although, I guess spotting a substitution isn't always obvious either). I guess it all just comes down to the method I choose on the day, assuming there is a choice.

Anyway, I've derailed the poor OPs thread enough, I'd best be off .

I think the discussion probably benefited the OP in some way. The give away for that substitution is that there is no 'y' term so you can definitely knock the ODE down by one order at least.

I think I remember asking my teacher this a while back and he said that although my suggestion was valid that sometimes they make you go through the PI and CF stuff (I do edexcel).

I genuinely don't believe that to be true. In my spec (OCR) we do touch on the use of substitution in ODEs so I'm sure it's a perfectly valid technique for the exam. Unless the question explicitly is broken down into parts i.e. find and solve the auxiliary equation, and hence find the complementary function. Then the next part asks you to find the particular integral etc.

If the question is not quite so structured and 'hand-holdy' then any valid method using a substitution should be fine.