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Question 1 (CLO (1): S marks A) : [2.5 Marks ] In the following equations, the...
(1) (2+2+2 marks] For the following equations, give their order and state whether they are linear...
(1) (2+2+2 marks] For the following equations, give their order and state whether they are linear or nonlinear. Briefly explain your answer (a) x+y" + xy' + (x2 – v2)y=0 where v is a parameter (b) më+ ki = ač – bì3 where m, k, a, b are constants (c) T = -k(T – A) where k, A are constants. (2) [3+3+4 marks] Consider the equation ay = y(y2 – 4u) where u is a parameter. (a) For u =...
1. (a) Express the following system of equations in augmented matrix form. 2x - 4y +...
1. (a) Express the following system of equations in augmented matrix form. 2x - 4y + 5z = 9 x + 3y + 8z = 41 6x + y - 3z = 25 (2 marks) (6) Use Gaussian elimination to solve the system of equations. (6 marks) 2. Given that a matrix A: 18 A= 1 8 -1 4 -1 -1 -1 8 (a) Determine AT. (6) Calculate the det (A). (2 marks) (6 marks) 3. Refer to the graph...
2nd order linear homogeneous Find the general solution to the following homogeneous differential equations (you answers...
2nd order linear homogeneous
Find the general solution to the following homogeneous differential equations (you answers must have two arbitrary constants (you may use any letters, for example p and q or m and n instead of ki and k2 - notation doesn't matter here]). y" + 2y' – 3y = 0 (b) 6y" – y-y=0 (c) y" + 5y = 0 (d) y" - 9y' +9y 0 The two constants, e.g. ki and k2, determine (and are determined by)...
non-homo 2nd order linear equations 1. Find the general solution for each of the following differential...
non-homo 2nd order linear equations
1. Find the general solution for each of the following differential equations (10 points each): (a) (b) (e) y" – 2y! - 3y = 3e2x y" — y' – 2y = -2.3 + 4.2? y" + y’ – 67 = 1234 + 12e-2x y" – 2y' – 3y = 3.ce-1 y" + 2y' + y = 2e- (Hint: you'll use Rule 7. at least once) (e 2. Find the solution to the following differential equation...
Question 1: (5 marks) Consider a two-species model for populations Ni and N2 follows as N1 (a -bN1 cN2) dt N2 (d -...
Question 1: (5 marks) Consider a two-species model for populations Ni and N2 follows as N1 (a -bN1 cN2) dt N2 (d - eN2 - Ni) dt (a) What kind of interaction does this system of equations represent? (b) Show that the equations can be simplified to dn1 an n1 (1 d7 dn2 Bn2 (1n2-n1). dT mT into the system of equations and picking by substituting N = kn\, N2 = ln2 and t appropriate constants k, l and m...
1. Consider the following system of linear equations: (8 marks) x+y = 3 7 7 2...
1. Consider the following system of linear equations: (8 marks) x+y = 3 7 7 2 -x+z=2 y-w=1 W = 4 z + w = 4 1) Use Gauss-Jordan elimination to put the augmented matrix corresponding to this system into reduced row echelon form. Clearly show all the elementary row operations applied. (3 marks) 12 nn
. Question 1 (40 marks) This question asks you to demonstrate your understanding of the following...
. Question 1 (40 marks) This question asks you to demonstrate your understanding of the following learning objectives LO 1.6 Express the Laplace Transform of common mathematical functions and linear ordinary differential equations using both first principles and mathematical tables. LO 1.7 Construct transfer functions for linear dynamic systems from (i) differential equations and (ii) reduction of block diagrams. LO1.8 Determine the time response of a Linear SISO system to an arbitrary input and having arbitrary initial conditions. LO 1.9...
Question 4 a) Solve the Initial value problem. (PLO-3, CLO-3,C3) Marks-13 (x+1) - ny =e(x+1)n+1, y(0)=1...
Question 4 a) Solve the Initial value problem. (PLO-3, CLO-3,C3) Marks-13 (x+1) - ny =e(x+1)n+1, y(0)=1 dx b) Solve the following non-linear first order ordinary differential equation. yp+ (x – y)p- xy = 0 (PLO-4, CLO-4,C4) Marks-12
Please find y(1.4) Question Question 12 (3 marks) Special Attempt 1 A system of two first order differential equations c...
Please find y(1.4)
Question Question 12 (3 marks) Special Attempt 1 A system of two first order differential equations can be written as A second order explicit Runge-Kutta scheme for the system of two first order equations is k1hn,un,vn), un+1 Consider the following second order differential equation d-y + 2 y-9y with y(1) and y'(1) 4 1. , Use the Runge-kutta scheme to find an approximate solution of the second order differential equation, at x-1.4, if the step size h...
1. (5 marks) The following equations were estimated using the data in “bwght": bwght=4.682 -0.005cigs, +0.155parity;+0.026male;+0.062white;...
1. (5 marks) The following equations were estimated using the data in “bwght": bwght=4.682 -0.005cigs, +0.155parity;+0.026male;+0.062white; (0.016) (0.0008) (0.006) (0.010) (0.012) n=1,388, R2=0.045, RP=0.043 and bwght=4.668 - 0.005cigs, +0.171parity;+0.033male;+0.049white;-0.002motheduc;+0.004fatheduci (0.036) (0.001) (0.006) (0.011) (0.015) (0.003) (0.003) n=1,191, R=0.048, RP=0.043 The variables' definition can be found in the link: http://fmwww.bc.edu/ec-p/data/wooldridge/bwght.des. i (2 marks) Considering the second regression results, comment on the estimated effect and statistical significance of fatheduc.(i.e., comment on the practical and statistical significance of fatheduc's partial effect separately) (3...
(1) (2+2+2 marks] For the following equations, give their order and state whether they are linear or nonlinear. Briefly explain your answer (a) x+y" + xy' + (x2 – v2)y=0 where v is a parameter (b) më+ ki = ač – bì3 where m, k, a, b are constants (c) T = -k(T – A) where k, A are constants. (2) [3+3+4 marks] Consider the equation ay = y(y2 – 4u) where u is a parameter. (a) For u =...
1. (a) Express the following system of equations in augmented matrix form. 2x - 4y + 5z = 9 x + 3y + 8z = 41 6x + y - 3z = 25 (2 marks) (6) Use Gaussian elimination to solve the system of equations. (6 marks) 2. Given that a matrix A: 18 A= 1 8 -1 4 -1 -1 -1 8 (a) Determine AT. (6) Calculate the det (A). (2 marks) (6 marks) 3. Refer to the graph...
2nd order linear homogeneous
Find the general solution to the following homogeneous differential equations (you answers must have two arbitrary constants (you may use any letters, for example p and q or m and n instead of ki and k2 - notation doesn't matter here]). y" + 2y' – 3y = 0 (b) 6y" – y-y=0 (c) y" + 5y = 0 (d) y" - 9y' +9y 0 The two constants, e.g. ki and k2, determine (and are determined by)...
non-homo 2nd order linear equations
1. Find the general solution for each of the following differential equations (10 points each): (a) (b) (e) y" – 2y! - 3y = 3e2x y" — y' – 2y = -2.3 + 4.2? y" + y’ – 67 = 1234 + 12e-2x y" – 2y' – 3y = 3.ce-1 y" + 2y' + y = 2e- (Hint: you'll use Rule 7. at least once) (e 2. Find the solution to the following differential equation...
Question 1: (5 marks) Consider a two-species model for populations Ni and N2 follows as N1 (a -bN1 cN2) dt N2 (d - eN2 - Ni) dt (a) What kind of interaction does this system of equations represent? (b) Show that the equations can be simplified to dn1 an n1 (1 d7 dn2 Bn2 (1n2-n1). dT mT into the system of equations and picking by substituting N = kn\, N2 = ln2 and t appropriate constants k, l and m...
1. Consider the following system of linear equations: (8 marks) x+y = 3 7 7 2 -x+z=2 y-w=1 W = 4 z + w = 4 1) Use Gauss-Jordan elimination to put the augmented matrix corresponding to this system into reduced row echelon form. Clearly show all the elementary row operations applied. (3 marks) 12 nn
. Question 1 (40 marks) This question asks you to demonstrate your understanding of the following learning objectives LO 1.6 Express the Laplace Transform of common mathematical functions and linear ordinary differential equations using both first principles and mathematical tables. LO 1.7 Construct transfer functions for linear dynamic systems from (i) differential equations and (ii) reduction of block diagrams. LO1.8 Determine the time response of a Linear SISO system to an arbitrary input and having arbitrary initial conditions. LO 1.9...
Question 4 a) Solve the Initial value problem. (PLO-3, CLO-3,C3) Marks-13 (x+1) - ny =e(x+1)n+1, y(0)=1 dx b) Solve the following non-linear first order ordinary differential equation. yp+ (x – y)p- xy = 0 (PLO-4, CLO-4,C4) Marks-12
Please find y(1.4)
Question Question 12 (3 marks) Special Attempt 1 A system of two first order differential equations can be written as A second order explicit Runge-Kutta scheme for the system of two first order equations is k1hn,un,vn), un+1 Consider the following second order differential equation d-y + 2 y-9y with y(1) and y'(1) 4 1. , Use the Runge-kutta scheme to find an approximate solution of the second order differential equation, at x-1.4, if the step size h...
1. (5 marks) The following equations were estimated using the data in “bwght": bwght=4.682 -0.005cigs, +0.155parity;+0.026male;+0.062white; (0.016) (0.0008) (0.006) (0.010) (0.012) n=1,388, R2=0.045, RP=0.043 and bwght=4.668 - 0.005cigs, +0.171parity;+0.033male;+0.049white;-0.002motheduc;+0.004fatheduci (0.036) (0.001) (0.006) (0.011) (0.015) (0.003) (0.003) n=1,191, R=0.048, RP=0.043 The variables' definition can be found in the link: http://fmwww.bc.edu/ec-p/data/wooldridge/bwght.des. i (2 marks) Considering the second regression results, comment on the estimated effect and statistical significance of fatheduc.(i.e., comment on the practical and statistical significance of fatheduc's partial effect separately) (3...
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