Differential Equations 11. Which ordinary differential equation below is equivalent to the following system of linear...
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).
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
(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.
2. Transform the following differential equation into an equivalent system of first-order differential equations -3° - 4x' +2.? = 2 cos 4t L M e e 00 O TI
4. Solve the nonhomogeneous linear system of differential equations 2. Solve the nonhomogeneous linear system of anerential equations () u-9" (). 3. Solve the homogeneous linear system of differential equations 1 ( 2 ) uten ( 46 ) + ( ). 4. Solve the nonhomogeneous linear system of differential equations 43,742 cos(46) - 4 sin(40) (10 5 cos(40) ) +847, 7 4cos(46) + 2 sin(40) 5 sin(46) 5. Solve the initial value problem for the nonhomogeneous linear system of differential...
A linear, time-invariant system is modeled by the ordinary differential equation y(t) + 7y(t) = 14f(t) Let f(t) = e^-t cos(2t)u(t) and y(0-) = -1. (a) Find the transfer function of the system and place your answer in the standard form H(s) = bms^m + bm-1s^m-1 + ... + b1s + bo / s^n + an-1s^n-1 + ... + a1s + a0 (b) Determine the output of the system as Y(s) = Yzs(s) + Yzi(s) and place both the zero...
State the order of the following ordinary differential equations and classify them as linear or non-linear. (2t-e2t) day +64 dy dt4 dt = - ye-66 + 2sin(5t) The order of the differential equation is and it is ---Select--- d²f dp2 = pln(-6p) + 2e5p The order of the differential equation is and it is ---Select--- day sinh( ) – In(6) dy dx = 2cos(5y) – y dx2 The order of the differential equation is and it is ---Select---
Consider a second order linear time invariant system represented by the following ordinary differential equation: 4. dx(t) dt dt dt Y (s) X(s) a. Find the transfer function H(s) of the system. (5 Points)
Consider the system of linear differential equations z,(t)-17/11 z(t) + 9/11 y(t) y,(t)-18/11 z(t) + 38/11 y(t) a) Find the equation of the x-nullcline. Write your answer as an equation in z and y Answer b) Find the equation of the y-nullcline. Write your answer as an equation of z and y Answer. c) The nullclines divide the plane into four regions as illustrated below. 忽聡 2 -2 2 -2 For each of the regions, determine the direction of the...