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3. Consider the following system of equations (a) Check if the explicit functions, y,-hi (ri,T2) ...
2. Consider the following two equations where all the parameters are non-zero. The two variables ri and r2 are assumed...
2. Consider the following two equations where all the parameters are non-zero. The two variables ri and r2 are assumed to be exogenous (a) Write down conditions under which the system is simultaneous equations system (2 marks) (b) Suppose the conditionsin (a) hold. What is the identification status of y equa tion (first equation)? How about the identification status of y2 equation (second equation)? (4 marks)
2. Consider the following two equations where all the parameters are non-zero. The two...
Consider the parametric equations below. x = 2 + 4t y = 1-t2
Consider the parametric equations below. x = 2 + 4t y = 1-t2 (a) Sketch the curve by using the parametric equations to plot points. Indicate with an arrow the direction in which the curve is traced as t increases.(b) Eliminate the parameter to find a Cartesian equation of the curve. y = _______ Consider the parametric equations below. x = 3t - 5 y = 2t + 4 (a) Sketch the curve by using the parametric equations to plot points. Indicate with an arrow the...
3. Consider the following stiff system of autonomous ordinary differential equations du f(u, u) =-3u +3,...
3. Consider the following stiff system of autonomous ordinary differential equations du f(u, u) =-3u +3, u(0)2 = ' dt de g(u, v) -2000u - 1000, v(0)-3 Note that 1 u<2 and -4 <v < 3 for all t. (a) Find the Jacobian matrix for the system of equa tions (b) Find the eigenvalues of the Jacobian matrix. (c) In the figure the shaded region shows the region of absolute stability, in the complex h plane, for third order explicit...
please explain every step. thanks Consider the following system of linear equations ri (a) For what...
please explain every step. thanks
Consider the following system of linear equations ri (a) For what values of r and s is this system of linear equations inconsistent? (b) For what values of and s does this system of linear equations have infinitely many solutions? (ey For what values of and s does this system of linear equations have a unique solution?
A system of two first order differential equations can be written as: A second order explicit R...
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 Consider the following second order differential equation: Use the Runge-kutta scheme to find an approximate solution of the second order differential equation, at x = 0.2, if the step size h = 0.1. Maintain at least eight decimal digit accuracy throughout all your calculations. You may express your answer as a five decimal...
T2 2t 2) Consider the vector functions x1) (t)- (a) In what intervals they are linearly independe...
t2 2t 2) Consider the vector functions x1) (t)- (a) In what intervals they are linearly independent? (b) Is it true that they are fundamental solution set of a linear 2 x 2-system 1c) and t interval I-(-5,16)? If yes, find the related linear system (c) The same question from (b) but on the interval 1 = (1,00).
t2 2t 2) Consider the vector functions x1) (t)- (a) In what intervals they are linearly independent? (b) Is it true that...
A system of two first order differential equations can be written as 0 dc A second order explicit...
A system of two first order differential equations can be written as 0 dc A second order explicit Runge-Kutta scheme for the system of two first order equations is Consider the following second order differential equation 7+4zy 4, with y(1)-1 and y'(1)--1. Use the Runge-kutta scheme to find an approximate solution of the second order differential equation, at x = 1.2, if the step size h Maintain at least eight decimal digit accuracy throughout all your calculations You may express...
Consider the non-linear system y-y(1-x-y). (a) Find equations for all of the x- and y-nullclines....
Consider the non-linear system y-y(1-x-y). (a) Find equations for all of the x- and y-nullclines. (b) Find the coordinates of each equilibrium point of the system. (c) Sketch the nullclines in the phase plane. Clearly mark the equilibrium points. Also indicate the direction of flow on the nullclines.
Consider the non-linear system y-y(1-x-y). (a) Find equations for all of the x- and y-nullclines. (b) Find the coordinates of each equilibrium point of the system. (c) Sketch the nullclines in the...
LARLALUI 2.5.021. MY Consider the following. x2 + y2 - 81 (a) Find two explicit functions...
LARLALUI 2.5.021. MY Consider the following. x2 + y2 - 81 (a) Find two explicit functions by solving the equation for y in terms of x. (positive function) X Y2 = (negative function) Y V
Question 3 Consider the following linear system of differential equations dx: = 2x-3y dt dy dt (a) Write this system of...
Question 3 Consider the following linear system of differential equations dx: = 2x-3y dt dy dt (a) Write this system of differential equations in matrix form (b) Find the general solution of the system (c) Solve the initial value problem given (0) 3 and y(0)-4 (d) Verify the calculations with MATLAB
Question 3 Consider the following linear system of differential equations dx: = 2x-3y dt dy dt (a) Write this system of differential equations in matrix form (b) Find the...
2. Consider the following two equations where all the parameters are non-zero. The two variables ri and r2 are assumed to be exogenous (a) Write down conditions under which the system is simultaneous equations system (2 marks) (b) Suppose the conditionsin (a) hold. What is the identification status of y equa tion (first equation)? How about the identification status of y2 equation (second equation)? (4 marks)
2. Consider the following two equations where all the parameters are non-zero. The two...
3. Consider the following stiff system of autonomous ordinary differential equations du f(u, u) =-3u +3, u(0)2 = ' dt de g(u, v) -2000u - 1000, v(0)-3 Note that 1 u<2 and -4 <v < 3 for all t. (a) Find the Jacobian matrix for the system of equa tions (b) Find the eigenvalues of the Jacobian matrix. (c) In the figure the shaded region shows the region of absolute stability, in the complex h plane, for third order explicit...
please explain every step. thanks
Consider the following system of linear equations ri (a) For what values of r and s is this system of linear equations inconsistent? (b) For what values of and s does this system of linear equations have infinitely many solutions? (ey For what values of and s does this system of linear equations have a unique solution?
t2 2t 2) Consider the vector functions x1) (t)- (a) In what intervals they are linearly independent? (b) Is it true that they are fundamental solution set of a linear 2 x 2-system 1c) and t interval I-(-5,16)? If yes, find the related linear system (c) The same question from (b) but on the interval 1 = (1,00).
t2 2t 2) Consider the vector functions x1) (t)- (a) In what intervals they are linearly independent? (b) Is it true that...
A system of two first order differential equations can be written as 0 dc A second order explicit Runge-Kutta scheme for the system of two first order equations is Consider the following second order differential equation 7+4zy 4, with y(1)-1 and y'(1)--1. Use the Runge-kutta scheme to find an approximate solution of the second order differential equation, at x = 1.2, if the step size h Maintain at least eight decimal digit accuracy throughout all your calculations You may express...
Consider the non-linear system y-y(1-x-y). (a) Find equations for all of the x- and y-nullclines. (b) Find the coordinates of each equilibrium point of the system. (c) Sketch the nullclines in the phase plane. Clearly mark the equilibrium points. Also indicate the direction of flow on the nullclines.
Consider the non-linear system y-y(1-x-y). (a) Find equations for all of the x- and y-nullclines. (b) Find the coordinates of each equilibrium point of the system. (c) Sketch the nullclines in the...
LARLALUI 2.5.021. MY Consider the following. x2 + y2 - 81 (a) Find two explicit functions by solving the equation for y in terms of x. (positive function) X Y2 = (negative function) Y V
Question 3 Consider the following linear system of differential equations dx: = 2x-3y dt dy dt (a) Write this system of differential equations in matrix form (b) Find the general solution of the system (c) Solve the initial value problem given (0) 3 and y(0)-4 (d) Verify the calculations with MATLAB
Question 3 Consider the following linear system of differential equations dx: = 2x-3y dt dy dt (a) Write this system of differential equations in matrix form (b) Find the...
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