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today Ive got a nice differential equation to explore so were going to look at the differential equation y equals y prime plus y double prime plus y triple prime plus y quadruple Prime and so on and so forth so its this infinite sum on the right hand side and were going to solve this two different ways were going to do a straightforward solution first then were going to do a bit of a sketchy solution and after all thats done Im going to leave you with two things one is like a question pertaining to the number of solutions of this differential equation and another is like a slight generalization of this type of differential equation and I think both of these things are fairly interesting okay so lets get started with our straightforward solution so Im going to maybe copy this differential equation over here you can take this right hand side and rewrite it as y prime plus the derivative with respect to X of Y prime plus y double prime plus y triple prime plus dot dot dot and t

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The easiest way to finish a page (and create a new one) is the \newpage command. This will add enough vertical space to fill the current page, and then add a page break. (You will need at least two LaTeX runs to see the full table of contents.)

In general, the command \\ signifies a line break and within the correct math mode environment, it can start a new equation line. Try the example on the right which sets the same multiple equations in several ways.

In general, the command \\ signifies a line break and within the correct math mode environment, it can start a new equation line.

At the end of an equation, if you want to start another equation immediately, press Shift+Enter instead of Enter. Each line will appear in a separate equation box, but theyll all be part of a single display paragraph.

The \\ command tells LaTeX to start a new line. It has an optional argument, extra-space , that specifies how much extra vertical space is to be inserted before the next line.

There are two commands to insert page breaks, clearpage and newpage . Below is an example using clearpage . If the command \clearpage is used, and there are stacked floating elements, such as tables or figures, they will be flushed out before starting the new page.

The \pagebreak command tells LaTeX to break the current page at the point of the command. With the optional argument, number , you can convert the \pagebreak command from a demand to a request. The number must be a number from 0 to 4. The higher the number, the more insistent the request is.

So lets review: RULE #1: you can add, subtract, multiply and divide by anything, as long as you do the same thing to both sides of the equals sign. RULE #2: to move or cancel a quantity or variable on one side of the equation, perform the opposite operation with it on both sides of the equation.

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