QUESTION 7 A solution of a homogeneous differential equation with constant coefficient is given by y...
2017, Q3. QUESTION 3 Determine whether the differential equation homogeneous and find its general solution. (150 marks total) y" +3 +2У = 5 sinx is homogeneous or non- QUESTION 3 Determine whether the differential equation homogeneous and find its general solution. (150 marks total) y" +3 +2У = 5 sinx is homogeneous or non-
Find the solution to this linear, second order, homogeneous, constant coefficient differential equation: 4y" + 12y' + 9y = 0
(1 point) Given the third order homogeneous constant coefficient equation y" + 3y" + 3y + y = 0 1) the auxiliary equation is ar3 + br2 + cr + d = ^3+3r^2+3r+1 - = 0. 2) The roots of the auxiliary equation are -1,-1,-1 (enter answers as a comma separated list). 3) A fundamental set of solutions is e^(-x),xe^(-x),x^2e^(-x) (enter answers as a comma separated list). 4) Given the initial conditions y(0) = -1, ý (0) = 2 and...
8. (9 points) Suppose the characteristic equation of a certain twentieth order, linear, constant coefficient, homogeneous differential equation has roots: 2,0, a, 2+3i, ti, +4i, ti, 2, 3, a, 2+3i ,2,3,0, and -3. (where a is a real constant) Write the general solution to this differential equation. (Do not attempt to solve for the coefficients).
Alinear constant coefficient differential equation is given by dyt) + dy ) + cy(t) = 0 Compute the homogeneous solution, yn (t), given that b=8, c=2 and initial conditions y(0) = CO and 490 = c. Given that the initial conditions are co = 0 and ci = 1, evaluate your homogeneous solution at the time t=7 8. Your solution should be the value y(7.8) which is the homogeneous solution evaluated at t=7.8. Make sure you type in a solution...
2. a) (7 pnts) Solve the second order homogeneous linear differential equation y" - y = 0. b) (6 pnts) Without any solving, explain how would you change the above differential equation so that the general solution to the homogeneous equation will become c cos x + C sinx. c) (7 pnts) Solve the second order linear differential equation y" - y = 3e2x by using Variation of Parameters. 5. a) (7 pnts) Determine the general solution to the system...
(3 points) Given the fourth order homogeneous constant coefficient equation y"" + 10y" + 9y-0 1) the auxiliary equation is ar br3+ cr2 + dr +e 2) The roots of the auxiliary equation are (enter answers as a comma separated list) 3) A fundamental set of solutions is Enter the fundamental set as a commas separated list yi , y2,y, y4). Therefore the general solution can be written as ycy c232 +c3ys c4y4- 4) Use this to solve the IVP...
Write a second order, constant-coefficient, homogeneous, linear differential equation in y which has a single critical point y = 0 and for which the phase portrait is a spiral source. y+
(17 points) A 9th order, linear, homogeneous, constant coefficient differential equation has a characteristic equation which factors as follows. (P2 - 2r+2) rtr + 3) = 0 Write the nine fundamental solutions to the differential equation. y y2 > Y4= Ys = Y y = 19 = (You can enter your answers in any order.)
(1 point) Given the fourth order homogeneous constant coefficient equation y' + 10y" + 9y = 0 1) the auxiliary equation is ar4 + bp3 + cp2 + dr te= r^(4)+10r^2+9 0. 2) The roots of the auxiliary equation are 1,-1,31,-3i (enter answers as a comma separated list). 3) A fundamental set of solutions is cosx,sinx,cos(3x), sin(3x) (Enter the fundamental set as a commas separated list 41, 42, 43, 44). Therefore the general solution can be written as y =...