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Unformatted text preview: Home > My Assignments > Section 7.7 (Homework) About this Assignment SMALL BRIAN DIXON MA 241, section 009, Fall 2005 Instructor: Drew Pasteur North Carolina State University Due: Tuesday, October 25, 2005 11:05 PM EDT Description Second-Order Linear Current Score: 14 out of 14 Equations Question Score pts subs 1 1/1 1/20 2 0.5/0.5 1/20 1.5/1.5 Viewing: Last Response View: All Responses Notes 1. [SCalcCC2 7.7.04.] Solve the differential equation. 2y'' - y' - y = 0 (a) Find the auxiliary equation using the variable r. 2r^2 - r - 1 [2r^2 - r - 1] = 0 (b) Determine the general solution. (_) (_) none of these (_) (_) (o) (o) (_) (_) (_) (_) pts subs 1 1/1 1/20 2 0.5/0.5 1/20 1.5/1.5 Viewing: Last Response View: All Responses Notes 2. [SCalcCC2 7.7.06.] Solve the differential equation. 5y'' = 7y' (a) Find the auxiliary equation using the variable r. 5r^2-7r [5r^2-7r] = 0 (b) Determine the general solution. (o) (o) (_) (_) (_) (_) none of these (_) (_) (_) (_) pts subs 1 1/1 1/20 2 0.5/0.5 1/20 1.5/1.5 Viewing: Last Response View: All Responses Notes 3. [SCalcCC2 7.7.08.] Solve the differential equation. 9y'' + 12y' + 4y = 0 (a) Find the auxiliary equation using the variable r. 9r^2+12r+4 [9r^2 + 12r + 4] = 0 (b) Determine the general solution. (_) (_) (_) (_) none of these (_) (_) (o) (o) (_) (_) pts subs 1 1/1 1/20 2 0.5/0.5 1/20 1.5/1.5 Viewing: Last Response View: All Responses Notes 4. [SCalcCC2 7.7.10.] Solve the differential equation. 25y'' + 16y = 0 (a) Find the auxiliary equation using the variable r. 25r^2+16 [25r^2 + 16] = 0 (b) Determine the general solution. (_) (_) (_) (_) (_) (_) (o) (o) (_) (_) none of these pts subs 1 2/2 1/20 2/2 5. [SCalcCC2 7.7.18.] Solve the initial-value problem. Viewing: Last Response View: All Responses Notes pts subs 1 2/2 1/20 2/2 Viewing: Last Response View: All Responses Notes pts subs 1 2/2 1/20 2/2 Viewing: Last Response View: All Responses Notes pts subs 1 2/2 1/20 2/2 Viewing: Last Response View: All Responses Notes y'' - 4y = 0 , y(0) = 1 , y'(0) = 0 y = (1/2)exp(2x)+(1/2)exp(-2x) [(1/2)*(exp(-2x) + exp(2x))] 6. [SCalcCC2 7.7.20.] Solve the initial-value problem. y'' + 4y' + 6y = 0 , y(0) = 2 , y'(0) = 4 y = exp(-2*x)*(2*cos(2^(1/2)*x)+4*sin(2^(1/2)*x)*2^(1/2)) 2x)*(2*cos(sqrt(2)x) + 4sqrt(2)*sin(sqrt(2)x))] [exp(- 7. [SCalcCC2 7.7.22.] Solve the initial-value problem. y'' - 2y' + y = 0 , y(2) = 0 , y'(2) = 1 y = -2exp(-2+x)+xexp(-2+x) [(x-2)*exp(x-2)] 8. [SCalcCC2 7.7.26.] Solve the boundary-value problem. y'' + 5y' - 6y = 0 , y(0) = 0 , y(2) = 1 y = -0.135335exp(-6x)+0.135335exp(x) (exp(x)-exp(-6x))] [(exp(2)-exp(-12))^(-1) * Home My Assignments ...
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