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[Music] today were going to look at a pretty nice functional differential equation now functional equations are common in math contexts and of course differential equations have numerous applications in the physical sciences as well as the biological sciences and engineering and there are standard undergraduate courses in differential equations but functional differential equations are more of a niche topic and in fact its kind of a hard subject that being said this functional differential equation well look at has some fairly nice Solutions we wont find all of them because I believe that there are infinitely many different types of solutions but we will explore this one equation okay so lets see what we have well explore this functional differential equation defined by F of 2x equals F Prime of x times F double Prime of x and well look at three special types of solutions a polynomial solution an exponential solution and a trigonometric solution and then look at a power series
