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Unformatted text preview: Home > My Assignments > Section 7.8 (Homework) About this Assignment SMALL BRIAN DIXON MA 241, section 009, Fall 2005 Instructor: Drew Pasteur North Carolina State University Due: Thursday, October 27, 2005 11:06 PM EDT Description Nonhomogeneous Current Score: 14.5 out of 16.5 Linear Equations Question Score pts 1 1/1 2 0.5/0.5 3 2/2 3.5/3.5 Viewing: Last Response View: All Responses Notes subs 1/20 1/20 1/20 1. [SCalcCC2 7.8.02.] Solve the differential equation using the method of undetermined coefficients. y'' + 9y = e3x (a) Find the auxiliary equation using the variable r. r^2+9 [r^2+9] = 0 (b) Determine the complementary solution. (_) (_) (_) (_) none of these (o) (o) (_) (_) (_) (_) (c) Find the general solution. y(x) = yc(x) + (1/18)*exp(3x) [(1/18)*exp(3x)] pts 1 1/1 2 0.5/0.5 3 2/2 3.5/3.5 subs 1/20 1/20 1/20 2. [SCalcCC2 7.8.06.] Solve the differential equation using the method of undetermined coefficients. y'' + 2y' + y = xe-x (a) Find the auxiliary equation using the variable r. r^2 + 2r + 1 [r^2 + 2r + 1] = 0 Viewing: Last Response View: All Responses Notes (b) Determine the complementary solution. (_) (_) none of these (_) (_) (_) (_) (_) (_) (o) (o) (c) Find the general solution. y(x) = yc(x) + (1/6)*x^3*exp(-x) [(1/6)*x^3*exp(-x)] pts subs 1 3/3 2/20 3/3 Viewing: Last Response View: All Responses Notes pts subs 1 3/3 2/20 3/3 Viewing: Last Response View: All Responses Notes pts 1 1/1 2 0.5/0.5 3 0/2 1.5/3.5 3. [SCalcCC2 7.8.08.] Solve the initial-value problem using the method of undetermined coefficients. y'' - 4y = excos(x) , y(0) = 1 , y'(0) = 2 y(x) = (9/8)*exp(2x) + (3/40)*exp(-2x) + exp(x)*(-1/5 cos(x) + 1/10 sin(x)) [(9/8)*exp(2x) + (3/40)*exp(-2x) + exp(x)*(-1/5 cos(x) + 1/10 sin(x))] 4. [SCalcCC2 7.8.10.] Solve the initial-value problem using the method of undetermined coefficients. y'' + y' - 2y = x + sin(2x) , y(0) = 1 , y'(0) = 0 y(x) = (17/15)*exp(x) + (1/6)*exp(-2x) - 1/2*x - 1/4 - 1/20 cos(2x) - 3/20 sin(2x) [(17/15)*exp(x) + (1/6)*exp(-2x) - 1/2*x - 1/4 - 1/20 cos(2x) - 3/20 sin(2x)] 5. [SCalcCC2 7.8.18.] Solve the differential equation using the method of undetermined coefficients or variation of parameters. y'' - 3y' + 2y = sin(x) (a) Find the auxiliary equation using the variable r. r^2 - 3r + 2 [r^2 - 3r + 2] = 0 subs 1/20 3/20 1/20 Viewing: Last Response View: All Responses Notes (b) Determine the complementary solution. (_) (_) (_) (_) (o) (o) (_) (_) none of these (_) (_) (c) Find the general solution. y(x) = yc(x) + (1/6)*exp(1.5x) (1/10)sin(x)] [(3/10)cos(x) + Home My Assignments ...
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