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as its equivalent system of first order equations 12. Write the given second order equation u"...
(1 point) Write the given second order equation as its equivalent system of first order equations....
(1 point) Write the given second order equation as its equivalent system of first order equations. u" – 1.5u - 1.5u = -7 sin(3), 4(1) = 5, (1) = 6.5 Use v to represent the "velocity function", i.e. v = u(t). Use v and u for the two functions, rather than u(t) and v). (The latter confuses webwork. Functions like sin(t) are ok.) u = Now write the system using matrices: and the initial value for the vector valued function...
(1 point) Write the given second order equation as its equivalent system of first order equations....
(1 point) Write the given second order equation as its equivalent system of first order equations. u" +5.5u' – 2.5u = -7.5 sin(3t), u(1) = -1, u'(1) = 0.5 Use v to represent the "velocity function", i.e. v=u't). Use v and u for the two functions, rather than u(t) and v(t)(The latter confuses webwork. Functions like sin(t) are ok.) u = V = Now write the system using matrices: and the initial value for the vector valued function is: u(1)
(1 point) If the differential equation d2x dt2 . dx + 6- m + 3x =...
(1 point) If the differential equation d2x dt2 . dx + 6- m + 3x = 0 dt is overdamped, the range of values for m is? (inf,3) Your answer will be an interval of numbers given in the form (1,2), (1,2), (-inf,6), etc. (1 point) Write the given second order equation as its equivalent system of first order equations. u" + 3 + 7u = 0 Use v to represent the "velocity function", i.e. V = u(t). Use v...
Find a first-order system of ordinary differential equations equivalent to the second-order nonlinear ordinary differential equation...
Find a first-order system of ordinary differential equations
equivalent to the second-order nonlinear ordinary differential
equation y ^-- = 3y 0 + (y 3 − y)
(3 points) Find a first-order system of ordinary differential equations equivalent to the second-order nonlinear ordinary differential equation y" = 3y' +(y3 – y).
Given the system of differential equations o y (7tcos(tut) Write the first order matrix different...
Given the system of differential equations o y (7tcos(tut) Write the first order matrix differential equation that is the basis for using Euler's method to compute the numerical solution. It is assumed you will use two auxiliary functions, xi and t2 Define the functions i and 2 in terms of v and y. E2 dri (t) dt 1(t) dr2(t) dt a2(t)
Given the system of differential equations o y (7tcos(tut) Write the first order matrix differential equation that is the...
Question 12 (3 marks) Special Attempt 2 A system of two first order differential equations can be written as 0 dr A second order explicit Runge-Kutta scheme for the system of two first order equation...
Question 12 (3 marks) Special Attempt 2 A system of two first order differential equations can be written as 0 dr A second order explicit Runge-Kutta scheme for the system of two first order equations is 1hg(n,un,vn), un+1 Consider the following second order differential equation d2 0cy-6, with v(1)-1 and y'()-o 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...
Problem 5. Consider the following second order linear differential equation f"(t)-f'(t) +f(t) kt ...
Problem 5. Consider the following second order linear differential equation f"(t)-f'(t) +f(t) kt which models a forced oscillation in a damping material. For example, imagine moving your hand back and forth underwater. Write this equation as a set of coupled first order equations by doing the following: ·Define a new function g = f'(t). This gives you one of the two coupled equations. . Use the given ODE, g, and its derivatives to write the second first order equation. Both...
(6 points) Find a first-order system of ordinary differential equations equivalent to the second-order ordinary differential...
(6 points) Find a first-order system of ordinary differential equations equivalent to the second-order ordinary differential equation Y" + 2y' + y = 0. From the system, find all equilibrium solutions, and determine if each equilibrium solution is asymptotically stable, or unstable.
consider 111 2+²y-dy' =-374 al write the equation abole as an equivalent system of first order...
consider 111 2+²y-dy' =-374 al write the equation abole as an equivalent system of first order differential equations. TET, +2 = 4², +3=y" luse b) express the system in matrix vector of equations formi 7 = Actix tgct)
problem 34 Equations with the Independent Variable Missing. If a second order differential equation has the...
problem 34
Equations with the Independent Variable Missing. If a second order differential equation has the form y"f(y, y), then the independent variable t does not appear explicitly, but only through the dependent variable y. If we let y', then we obtain dv/dt-f(y, v). Since the right side of this equation depends on y and v, rather than on and v, this equation is not of the form of the first order equations discussed in Chapter 2. However, if we...
(1 point) Write the given second order equation as its equivalent system of first order equations. u" – 1.5u - 1.5u = -7 sin(3), 4(1) = 5, (1) = 6.5 Use v to represent the "velocity function", i.e. v = u(t). Use v and u for the two functions, rather than u(t) and v). (The latter confuses webwork. Functions like sin(t) are ok.) u = Now write the system using matrices: and the initial value for the vector valued function...
(1 point) Write the given second order equation as its equivalent system of first order equations. u" +5.5u' – 2.5u = -7.5 sin(3t), u(1) = -1, u'(1) = 0.5 Use v to represent the "velocity function", i.e. v=u't). Use v and u for the two functions, rather than u(t) and v(t)(The latter confuses webwork. Functions like sin(t) are ok.) u = V = Now write the system using matrices: and the initial value for the vector valued function is: u(1)
(1 point) If the differential equation d2x dt2 . dx + 6- m + 3x = 0 dt is overdamped, the range of values for m is? (inf,3) Your answer will be an interval of numbers given in the form (1,2), (1,2), (-inf,6), etc. (1 point) Write the given second order equation as its equivalent system of first order equations. u" + 3 + 7u = 0 Use v to represent the "velocity function", i.e. V = u(t). Use v...
Find a first-order system of ordinary differential equations
equivalent to the second-order nonlinear ordinary differential
equation y ^-- = 3y 0 + (y 3 − y)
(3 points) Find a first-order system of ordinary differential equations equivalent to the second-order nonlinear ordinary differential equation y" = 3y' +(y3 – y).
Given the system of differential equations o y (7tcos(tut) Write the first order matrix differential equation that is the basis for using Euler's method to compute the numerical solution. It is assumed you will use two auxiliary functions, xi and t2 Define the functions i and 2 in terms of v and y. E2 dri (t) dt 1(t) dr2(t) dt a2(t)
Given the system of differential equations o y (7tcos(tut) Write the first order matrix differential equation that is the...
Question 12 (3 marks) Special Attempt 2 A system of two first order differential equations can be written as 0 dr A second order explicit Runge-Kutta scheme for the system of two first order equations is 1hg(n,un,vn), un+1 Consider the following second order differential equation d2 0cy-6, with v(1)-1 and y'()-o 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...
Problem 5. Consider the following second order linear differential equation f"(t)-f'(t) +f(t) kt which models a forced oscillation in a damping material. For example, imagine moving your hand back and forth underwater. Write this equation as a set of coupled first order equations by doing the following: ·Define a new function g = f'(t). This gives you one of the two coupled equations. . Use the given ODE, g, and its derivatives to write the second first order equation. Both...
(6 points) Find a first-order system of ordinary differential equations equivalent to the second-order ordinary differential equation Y" + 2y' + y = 0. From the system, find all equilibrium solutions, and determine if each equilibrium solution is asymptotically stable, or unstable.
consider 111 2+²y-dy' =-374 al write the equation abole as an equivalent system of first order differential equations. TET, +2 = 4², +3=y" luse b) express the system in matrix vector of equations formi 7 = Actix tgct)
problem 34
Equations with the Independent Variable Missing. If a second order differential equation has the form y"f(y, y), then the independent variable t does not appear explicitly, but only through the dependent variable y. If we let y', then we obtain dv/dt-f(y, v). Since the right side of this equation depends on y and v, rather than on and v, this equation is not of the form of the first order equations discussed in Chapter 2. However, if we...
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