1. Given y” + 3y' - 2y 0. Give the characteristic equation (the quadratic equation that...
(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
(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...
(1 point) Mark all of the possibilities that can arise when solving a quadratic equation as in the method of solving order 2 Cauchy-Euler equations. е A. One repeated real root. B. Two distinct real roots. C. No roots D. One complex root. E. Two complex roots. F. One real root and one complex root. G. None of the above (1 point) To find , and u, we would need to integrate which of the following? Mark all that apply....
1. Rewrite the 3rd order differential equation, y" - 2y" 3y' 4y 0 as a vector differential equation of the form v' = Av where A E Ms(R) is a matrix.
7. Consider the first order differential equation 2y + 3y = 0. (a) Find the general solution to the first order differential equation using either separation of variables or an integrating factor. (b) Write out the auxiliary equation for the differential equation and use the methods of Section 4.2/4.3 to find the general solution. (c) Find the solution to the initial value problem 2y + 3y = 0, y(0) = 4.
Differential Equation Roots rı, 12 General Solution y" - 6y' + 3y = 0 y" + 2y + 5y = 0 Y" +22y + 121y = 0
Consider the differential equation y" – 7y + 12 y = 0. (a) Find r1, 72, roots of the characteristic polynomial of the equation above. 11,2 M (b) Find a set of real-valued fundamental solutions to the differential equation above. yı(t) M y2(t) M (C) Find the solution y of the the differential equation above that satisfies the initial conditions y(0) = -4, y'(0) = 1. g(t) = M Consider the differential equation y" – 64 +9y=0. (a) Find r1...
Consider the following differential equation. 4x^2y′′+3xy′+14x^2y=0 Consider the following differential equation. (c) Find the series solution (x> 0) corresponding to the larger root. 7.15 (8k1)2 !-9-17 (4k+1)2 (-1) 14* k19.17.(4k1)2 y(r) = x1/14 | 1 + y(x) = x1/4 | 1 + Σ k!.7.15-..(4k + 1 ) 2 に! Consider the following differential equation. (c) Find the series solution (x> 0) corresponding to the larger root. 7.15 (8k1)2 !-9-17 (4k+1)2 (-1) 14* k19.17.(4k1)2 y(r) = x1/14 | 1 + y(x)...
Question 10 Find the differential equation of the given family y =C + 2 a)xy 3y +6=0 b) 2y-e-0 c)y+2y1=0 y+2y-1-0 d) y+2xy 1-0 f) None of the above. Question 11
6 (5) Solve the differential equation using a Laplace Transform: y 3y' +2y t y(0) 0, y'(0) 2