1. Rewrite the 3rd order differential equation, y" - 2y" 3y' 4y 0 as a vector...
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.
(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. Given y” + 3y' - 2y 0. Give the characteristic equation (the quadratic equation that finds the roots). (a) r2+ 3r - 2 = 0 (b) r2+ 3r + 2 = 0 (c) 2r2+ 3r - 1 = 0 (d) 2r2+ 3r + 1 = 0 (e) r2+r-2 = 0 (f) r2+r+ 2 = 0 (g) 2r2 +r-1=0 (h) 2r2+r+ 1 = 0 2. Find the larger root of the auxiliary equation of the differential equation y” + 3y...
Given the differential equation y" – 4y' + 3y = - 2 sin(2t), y(0) = -1, y'(0) = 2 Apply the Laplace Transform and solve for Y(8) = L{y} Y(S) -
#32 U. + 2y + y + 1 -e: y(0) = 0, y'(o) - 2 In Problems 31-36, determine the form of a particular solution for the differential equation. Do not solve. 31. y" + y = sin : + i cos + + 10' 32. y" - y = 2+ + te? + 1221 x" - x' - 2x = e' cos - + cost y" + 5y' + 6y = sin t - cos 2t 35. y" –...
Problem 1 1. Consider the third order equation 2 t²y' - 2y" -3t" Q. Write the equation above as an equivalent First order differential equations. Use x =Y , X2=4' and x3=y". system of b. express your system of equations in matrix vector form: = Alt) R + g(+)
For the differential equation y" + 4y' + 13y = 0, a general solution is of the form y = e-2x(C1sin 3x + C2cos 3x), where C1 and C2 are arbitrary constants. Applying the initial conditions y(0) = 4 and y'(0) = 2, find the specific solution. y = _______
Find the general solution of the given second-order differential equation. 27"-3y + 4y = 0 Upload a completed solution of your work as a PDF, JPEG or DOCX file. Upload Choose a File Question 5 Find the general solution for the given second order differential equation. - 64+25 y = 0 Please show all work and upload a file (PDF, JPG, DOCX) of the work and circle your final answer. Upload Choose a File
6 (5) Solve the differential equation using a Laplace Transform: y 3y' +2y t y(0) 0, y'(0) 2
Digital Signal Processing Homework #4 1. Find the solution of the differential equation: y+4y+3y = x+2x for x(t)-e'u(t) and initial conditions y(0) 0, (0) 1 What is the transfer function of a LTI system that is describable by the equation above? 2. Find the transfer functions of the LTI systems A and B in the configuration shown below when you are given that v v-z and y-x