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Section Math 1.1 Worksheet
Solutions
1. State the order of the differential equation and indicate the independent and dependent variables. Determine whether the differential equation is linear or nonlinear. (a) d2 y + xy = y dx2 The independent variable is x and the dependent variable is y. The differential d2 equation is second-order, linear dxy + (x - 1)y = 0 with variable coefficients. 2
(b)
d2 y +x y =y 2 dx The independent variable is x and the dependent variable is y. The differential equation is second-order, nonlinear. d3 r (c) + t2 = r tan t dt3 The independent variable is t and the dependent variable is r. The differential equa3r tion is third-order, linear d 3 + (- tan t) r = -t2 with variable coefficients. dt d2 X dX = 3uX + cos u 2 du du The independent variable u is and the dependent variable is X. The differential equation is second-order, nonlinear. d2 x dx (e) y 2 + y 3 + y = ey dy dy Be careful to note that the independent variable is y and the dependent variable is x. 2 The differential equation is second-order, linear y d x + y 3 dx = ey - y with variable dy 2 dy coefficients. du 4 (f) = 1 + v2 dv The independent variable is v and the dependent variable is u. The differential equation is first-order, nonlinear....