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Unformatted text preview: MA 2930, Jan 26, 2011 Worksheet 1 1. Write down in your own words what a differential equation is. What infor- mation does it give you? Can you think of at least two different ways of specifying a differential equation? A differential equation is a relation among a function and its derivatives. It tells you how the values of a function and its derivatives are related at any value of the independent variable. Two different ways of specifying a differential equation are via an algebraic equation and a direction field. 2. Suppose someone gives you the direction field of a differential equation. How would you find its solutions? Start at any point (corresponding to an initial value) and follow the ar- rows from that point on; youll get the solution (aka integral curve) passing through that point. 3. (a) Is the function y ( t ) = t a solution of y 000 + 4 y 00 + 3 y = t ? To check if it is a solution plug it into the two sides of the equation and see if they come out equal: if they do, it is a solution, otherwise its not. In the given problem the left hand side gives (...
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