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Unformatted text preview: Sample WeBWorK problems. 1.(1 pt) Suppose that the initial value problem has a solution in an interval about x 0. Find y 0 = . Find y 0 = . Find y 0 = . Note that for y 0 and y 0 you will have to differentiate the equation twice (remembering that y is a function of x) and back substitute the values given or already calculated. The Taylor polynomial of degree 3 of the solution about x 0 is T3 y x = . Correct Answers: 5 20 30 1 + 5*x + 10*x*x +5*x*x*x Muhammad Ulhaque WeBWorK assignment 1 due 1/20/08 at 11:55 PM. (3 * 9 * ln(x) + 3 * 16 * x + 77)**(1/3) WW Prob Lib1 02 Winter 2008 8 8 8*(1+0.777777777777778*exp(x**2/(2*2)))/(10.7777777 7.(1 pt) Consider the differential equation 8x 7 9y2 6 A set of implicit solutions of this equation is y3 y2 y x2 x C Now find the implictit solution of this equation subject to the initial condition y 2 2: y3 y2 y x2 x 0 Correct Answers: 3 0 6 3.(1 pt) Solve the initial value problem 4 dy 6 tan 3x y 4 sin 4x 0 y0 2 7 dx 3 The solution is y x 0 Correct Answers: 6 (160*cos(2 * x)  32*cos(10 * x)  160 *cos(4 * x) +672)/(320 * cos(3 * x)**2) 4 7 4.(1 pt) Find u from the differential equation and initial con38 dition. u Correct Answers: (1/4)*ln(78962960182679.4 + ((4/3)*2.71828182845905^(3*t))) dy 9 16x x dx xy2 with the initial condition: y 1 5 y Correct Answers: 0 5.(1 pt) Find the function y the differential equation y x (for x e3t 4u u0 du dt 8 8.(1 pt) 0 ) which satisfies 1 2 3 5
1 6 7 dy 3y x11 x 0 dx with the initial condition: y 1 2 y Correct Answers: 0.125*(x ** 11) + 2.125 * (x ** 3) x 2.(1 pt) Find the function y the differential equation y x (for x 0 ) which satisfies y y y 5x2 2y2 7 y0 1 6.(1 pt) Consider the differential equation 1 x 64 y2 32 This equation has the 2 constant solutions (in increasing order) y= and y= The solution of this equation subject to the initial condition 64 is y0 y= Correct Answers: 4 8 Sketch the direction field for the ODE Prepared by the WeBWorK group, Dept. of Mathematics, University of Rochester, c UR 2 in the range 5 x 5, 5 y 5. Do a good job, because you only get one shot at this problem. dy dx y2 2x2 20 100 From among the functions whose graphs are displayed above, select the one that is a solution to the differential equation. You can click on any image to enlarge it. Enter a number from 1 to 8. Correct Answers: 5 ...
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This note was uploaded on 06/09/2008 for the course MATH MATH 263 taught by Professor Humphire during the Spring '08 term at McGill.
 Spring '08
 Humphire

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