consider 111 2+²y-dy' =-374 al write the equation abole as an equivalent system of first order...
Problem 1 1. Consider the third order equation 2 t²y' - 2y" -3t" Q. Write the equation above as an equivalent First order differential equations. Use x =Y , X2=4' and x3=y". system of b. express your system of equations in matrix vector form: = Alt) R + g(+)
Problem 4. The higher order differential equation and initial conditions are shown as follows: = dy dy +y?, y(0) = 1, y'(0) = -1, "(0) = 2 dt3 dt (a) [5pts. Transform the above initial value problem into an equivalent first order differential system, including initial conditions. (b) [2pts.] Express the system and the initial condition in (a) in vector form. (c) [4pts.] Using the second order Runge Kutta method as follows Ū* = Ūi + hĚ(ti, Ūi) h =...
a) Consider the first-order differential equation (y + cos.r) dx + dy = 0. By multiplying integrating factor y(x) = ei" to both sides, show that the differential equation is exact. Hence, solve the differential equation. (6 marks) b) Solve the differential equation (4.r + 5)2 + ytan z = dc COSC (7 marks)
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).
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. Transform the following differential equation into an equivalent system of first-order differential equations 2-(3) – 3r(2) – 4.x' + 2x² = 2 cos 4t
2. Transform the following differential equation into an equivalent system of first-order differential equations 2-(3) – 3r(2) – 4.x' + 2x² = 2 cos 4t
Consider the system of two coupled differential equations: y-cx + dy, x-ax + by, with the equilibrium solution (xe,ye) = (0,0) (a) Rewrite the coupled system as a matrix differential equation and identify the matrix A. Obtain a general solution to the matrix differential equation in terms of eigenvectors and eigenvalues of A. Justify your answer (b) Classify possible types and stability of the equilibrium with dependence on the eigenvalues of A. (Note: You are not asked to compute the...
(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...
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...