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1. [10pts) A linear DE Ly=0 has auxiliary equation r (2r - 3)² = 0. If...
Suppose that the auxiliary equation of Ay (6)(x) + By (5) (x) + Cy(4) (x) + Dy'''(x) + Ey''(x) + Fy'(x) + Gy(x) = 0 has solutions of r : = -12 (with multiplicity 3), r = -12+3 i, and r = 13. Select all possible linearly independent solutions of the differential equation. Y = – 2 cos(3t) y = te3t – 12t – 9 sin(3t) = 9t²e = ly 13t 14te' у = y = 11e13t 12t ly =...
(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...
1. [10pts] (a) Solve for 2 > 0 the DE: 20%Y" + 102’y" +59xy' + 45y = 0. Answer: Solution: (b) Solve the DE in Part (a) for r <0.
(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 =...
Question 1 5 pts What is the order of the DE? Is the DE linear or nonlinear? 3 54' - (tan x)y= Vx+ +1 (7) 5.22 3rd order; nonlinear 2nd order; nonlinear 2nd order; linear 3rd order; linear LUCSLIUI 5 pts Is the function y=2e-32 - 4e5x a solution to the DE? Y' - 2y - 15y = 0 O No O Yes Question 3 5 pts Solve the separable DE. dy 3.cy + 2y - 15x - 10 dac...
3. [10pts] Consider the DE: xy" + 7xy' + Ty = 0. (a) Find the roots rı and r2 of the indicial equation of the DE (with rı >r2). r = r2 = Solution: (b) If we use Frobenius method to solve the DE, we obtain for the largest indicial root and for n > 0, a recurrence acn relation of the form Cn+1 where a and b are constants. Find a and b. m11
Please show all work: Suppose that the auxiliary equation of Ay (5) (z) + By (4) (z) + Cy" independent solutions of the differential equation. (z) + Dy (z) + Ey, (z) + Fy(z) = 0 has solutions of r = 7 (with multiplicity 2) r = 8 and r = 3 1 Select all possible linearly =-, 6e y = 500s(3)
please help and show steps 3. Solve the following IVP: ly'(0) = y'o, y(0) = yo where p > 0 and k 1. 2. Let k=0 Use the above power series to solve the following IVP. List the first six nonzero terms the solution the differential equation. ay = (t + y)2 ,y(0) = 0.
Problem 1 A and B Problem 1. For each differential equation below, rewrite it in operator form, give the associated homogeneous DE, and find the general solution to the associated ho- mogeneous DE. (a): y" - 65" + 25y = ?. (b): y" +64 +9y = 4e 37 Problem 2. Suppose the auxiliary equation associated with Ly) = F has three distinct real roots, r=a, r=b, r=c. Use the Wronskian to verify that the three solutions yı(x) = caz, 72(x)...
(10 points) For the differential equation y(6) - 2y (5) – 3y(4) + 2y(3) + 10y" – 8y = 0. Find the fundamental solution set to the DE if the characteristic equation in factored form is given by (r – 2) (r2 + 2r + 2) (r - 1) (r + 1) = 0