- #1

- 192

- 0

[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?

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- Thread starter matematikuvol
- Start date

- #1

- 192

- 0

[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

pasmith

Homework Helper

- 2,016

- 649

[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?

Because usually the first thing to do is divide by the coefficient of [itex]y''[/itex].

- #3

- 192

- 0

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

- #4

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- 1

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

My guess, the behavior of the solution set changes drastically wherever m(x)=0.

- #5

HallsofIvy

Science Advisor

Homework Helper

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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 "equi-potential 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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