I am not understanding how can I find the degree and order of this DE.
$e^{y'''} - xy'' +y = 0$
Should I bring ln here? Please solve for me if you can.
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No need to take ln - it won't simplify the equation. We rewrite the question in the form: $f(y^n,y^{n-1},...,y,x)$:
$$f(y''',y'',y,x) = e^{y'''} - xy'' + y = 0$$
The order of a DE is the order of the highest derivative of the dependent variable involved in the function $f$, so this is a 3rd order DE due to the term $e^{y'''}$.
The degree of a DE is the order of the highest derivative of thje dependent variable $f(y^n,y^{n-1},...,y,x)$ but only if $f$ is a polynomial with respect to the variables $y^n,y^{n-1},...,y$.
In the case of your equation, $f(y''',y'',y,x) = e^{y'''} - xy'' + y = 0$, we can see that f is NOT a polynomial w/r to the derivatives of y due to the term $e^{y'''}$. Therefore, the degree of your DE is undefined.
As an aside, I don't think the degree of a DE is a particularly useful concept mathematically speaking, but the order is important.
Derek O
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Thank you sir!! – Md Mosleh Uddin Jun 20 '20 at 04:37
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No problem - if you found my answer helpful, please consider accepting it, thank you! https://stackoverflow.com/help/someone-answers – Derek O Jun 20 '20 at 04:38
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Accepted sir... Sorry. I am new here.. I don't know all rules – Md Mosleh Uddin Jun 20 '20 at 04:40
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Sorry.. i made a mistake while typing – Md Mosleh Uddin Jun 20 '20 at 04:43
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Can u look another time on the question – Md Mosleh Uddin Jun 20 '20 at 04:44
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It is -xy" ... I mistakenly typed xy"'...sorry for that – Md Mosleh Uddin Jun 20 '20 at 04:45
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I updated my answer! – Derek O Jun 20 '20 at 05:00