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Coefficients derivative 
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#1
Dec1912, 06:35 AM

P: 192

Why we always write equation in form
[tex]y''(x)+a(x)y'(x)+b(x)=f(x)[/tex] Why we never write: [tex]m(x)y''(x)+a(x)y'(x)+b(x)=f(x)[/tex] Why we never write coefficient ##m(x)## for example? 


#2
Dec1912, 08:45 AM

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#3
Dec1912, 12:42 PM

P: 192

But what if for some ##x##, ##m(x)=0##.



#4
Dec2112, 05:27 AM

P: 428

Coefficients derivative



#5
Dec2112, 10:56 AM

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I'm not sure how to answer your question, "Why we never write coefficient m(x) for example?" because we often do! I suspect you simply have not yet gone far enough in differential equations to see such equations.
Of course, if m(x) is never 0, we can simplify by dividing by it. If m(x)= 0 for some x, that x becomes a "singular point" for the equation either a "regular singular point" or an "irregular singular point". Regular singular points can be handled in a similar way to "Euler type" or "equipotential equations, [itex]ax^2y''+ bxy'+ cy= f(x)[/itex] where each coefficient has x to the same degree as the order of the derivative. Such equations are typically approach late in a first semester differential equations class. 


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