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Unformatted text preview: Tufts University Mathematics 38 Department of Mathematics Spring 2006 Differential Equations: Review for Exam 1 PLEASE READ: This is meant to be a representative list of problems to help you prepare for the first midterm examination. It is not meant to be all-inclusive. There may be material on this review that is not on the midterm, and vice versa. 1. In your own words, define the following terms: (a) dependent variable (b) independent variable (c) order of a differential equation (d) linear differential equation (e) nonlinear differential equation (f) homogeneous linear differential equation (g) nonhomogeneous linear differential equation (h) linear differential equation with constant coefficients (i) linear differential equation with nonconstant coefficients (j) characteristic equation In each case, illustrate the correct use of these terms for a differential equation of your choice. 2. Find the general solution of the differential equation: x (ln x ) dy dx- 2 y =- ln x for x > 1, using both the method of integrating factors and the method of variation of...
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