(17 points) A 9th order, linear, homogeneous, constant coefficient differential equation has a characteristic equation which...
(17 points) A 9th order, linear, homogeneous, constant coefficient differential equation has a characteristic equation which factors as follows. (p2 + 4r + 8) ºr(r – 2)2 = 0 Write the nine fundamental solutions to the differential equation. Y1 = Y2 = Y3 = Y4 = Y5 = Y6 = 47 = Ys = Y9 = (You can enter your answers in any order.)
(17 points) A 9th order, linear, homogeneous, constant coefficient differential equation has a characteristic equation which factors as follows. (p2 + 6r + 18)ºr(r + 1)2 = 0 Write the nine fundamental solutions to the differential equation. Y1 = = Y2 = Y3 Y4 = Y5 = Y6 = = Y7 = Y8 = Y9 =
(17 points) A 9th order, linear, homogeneous, constant coefficient differential equation has a characteristic equation which factors as follows. (r? - 4r +13)*r(r + 3) = 0 Write the nine fundamental solutions to the differential equation. 99 (You can enter your answers in any order.)
2. You can use Dand write an operator instead of an equation in this question. (a) Find a constant coefficient linear homogeneous differential equation of lowest order that has n(x)-x , y2(z) = x2 , and y3(z) = eェamong its solutions. (b) Now find a different linear homogeneous differential equation of an order lower than the one in (a) that has the same y1,U2,U3 among its solutions. (c) Find a constant coefficient linear homogeneous differential equation of lowest order that...
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).
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+
(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...
Find the solution to this linear, second order, homogeneous, constant coefficient differential equation: 4y" + 12y' + 9y = 0
Two of the solutions of a linear homogeneous differential equation with constant coefficients are yi = -21%e-32 and Y2 = 4sin(31). What is the minimum possible order of the differential equation? 02 3 4 5 O 6 O 7
You are told that a certain second order, linear, constant coefficient, homogeneous ode has the solutions y1(x) = e^γx cos ωx, and y2(x) = e^γx sin ωx, where γ and ω are real-valued parameters and −∞ < x < ∞. 4. You are told that a certain second order, linear, constant coefficient, homogeneous ODE has the solutions where γ and w are real-valued parameters and-oo < x < oo. (a) Compute the Wronskian for this set of solutions. (b) Using...