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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