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4. (22 points) Write down the form of a particular solution to the equation (a) (10...
2 (6 points) Determine a suitable form for a particular solution of the differential equation y" + y 3 sint-1e-2 +t sin(2t) e. Do NOT determine a particular solution, just write the form that you will use when looking for one.
1. Find the general solution to the equation y" - y - 2y = -e- 2. Find a particular solution to y" + 4y = 11 sin(2t) + cos(2t) 3. Find the form of a particular solution to be used in the Method of Undetermined Coefficients for the equation y" + 2y' +2y = te-* cost Do not solve the equation
(1 point) Find a particular solution for each differential equation y" + 3y = 5t, then yp = y" - y = 3et sin(t), then yp = y" + 4y = cos(2t), then yp =
Match the differential equation with it's particular solution form. You MUST use the method of undetermined coefficients and you MUST show all work as to how you came to your conclusions. You have ONE (1) attempt at this problem 5t a. At’e -56 5t 4t b. Ate 5t 5t cđe Vy' + 2y' – 8y = (4t+5) - Vy' + 10y' + 25y = e - Vy" + 2y' – 8y = e y' + 2y' – Sy = (4t...
Determine the form of a particular solution of the equation. 4, NA+B+ Ct+D)+l u-AB2+C+D+ Ee13 up-A+ B+Ee13) Find the general solution of y" 14y' +58y 0. y- ce cos(31) +ce sin(3) y-ce cos(3t) + eze 'sin(31) y ce cos(3t) + ce"sin(3t) y-cje"cos(3t) + czesin(3t) -7t 7t Find the general solution ofy"-3'-28y-0. y(t) = cer + cze-41 Find the general solution ofy"- 130y 0. JC1 + c2e130r ycie +te130r Find the general solution of y"-30y' 225y 0. cote 15t 15t 15t...
Determine the form of a particular solution for the differential equation. Do not solve. y" - 18y' + 82y = et + tsin 2t - cos 2t The form of a particular solution is yp(t)= (Do not use d D. e. Ei or las arbitrary constants since these letters already have defined meanings.)
Problem 3: Insights into Differential Equations a. Consider the differential equation 습 +4 = f(t), where f(t) = e-u, 12 0. Please write the forms of the natural and forced solution for this differential equation. You DO NOT need to solve. (7 points) b. Again consider the differential equation f(t), where f(t) is an input and y(t) is the output (response) of interest. Please write the differential equation in state-space form. (10 points) c. The classical method for solving differential...
Determine the form of a particular solution for the differential equation. Do not solve. y" - 4y' + 5y = e 7 + t sin 6t - cos 6t The form of a particular solution is yp(t)- (Do not use d, D, e, E, I, or I as arbitrary constants since these letters already have defined meanings.)
Consider the nonhomogeneous second order linear equation of the form y" + 2y' + y = g(t). Given that the fundamental solution set of its homogeneous equation is {e**, te' } For each of the parts below, determine the form of particular solution y, that you would use to solve the given equation using the Method of Undetermined Coefficients. DO NOT ATTEMPT TO SOLVE THE COEFFICIENTS. a) y" + 2y' + y = 2te b) y" + 2y' + y...
Which of the following represents the form of the particular solution y, of the differential equation? y" + 2y' - 24y = 372 +2cos(51) Ovp = Ar? + Bcos(5t) + C O yp= Ar? +8sin(58) Yp - Al? + B+ + C + Dcos(5t) + Esin(58) Ovo - Ar+ Bcos(5t) + Csin(51)