{ i feel that this is Not a smart question and that it is about the basics of something , but i tried to find the that "something" to know about it myself but i couldn't , as i couldn't name the issue , so i couldn't know what to search about(adsbygoogle = window.adsbygoogle || []).push({});

that is why i'm asking here in a forum , so please don't be annoyed if it appeared to be a naive question , thank you :) }

i don't understand why did we change the formula so that only one variable is in it

would it matter if p(x) and r(x) are not constants ? (i.e : something like p(x)= -3/x^{2}) after all whether p(x) is a constant or -3/x^{2}it is after all a function of (x) , then i am on the right formula as the general formula of 2nd order ODE's y" + p(x) y'+ r(x) y= g(x) , right ?

these are 2 solutions (attached ) , mine (the wrong one) , and the other is the model answer (but i see it has an error , m should be 2±j√6 )

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# A solved 2nd order ODE that i don't understand its solution

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