We need at least 10 more requests to produce the answer.
0 / 10 have requested this problem solution
The more requests, the faster the answer.
Q1 (7 points) For k e R any constant, find the general solution to xa y"...
Question 2: (5+15=20 points) a) Find the value of the constant k e R for which the differential equation (2+ y + xy) dx + (1+2+kx*y) dy=0 is exact. b) Find the solution of the initial value problem using the value of k you found in part (a). (2+ y + r?y?)dr + (1 + x + k.xºy)dy = 0, y(0) = 2
2. (e) (7 points) Find a homogeneous linear differential equation with constant coefficients whose general solution is y = 4 + ce?* + Gxe7x.
(17 points) (a) Find the general solution of the differential equation y" (t) + 4y(t) = 0. general solution = (Use the letters A and B for any constants you have in your solution.) (b) For each of the following initial conditions, find a particular solution. (i) y(0) = 0, y'(0) = 1: y = (ii) y(0) = 1, y'(0) = 0:y= (iii) y(0) = 1, y(1) = 0:y= (iv) y(0) = 0, y(1) = 1: y = (On a...
Find the general solution of the second order constant coefficient linear ODEs 7. Find the general solution of the second order constant coefficient linear ODE. (a) y" +2y = 0 (b) 2y" – 3y +y=0 (c) y" – 2y – 2y = 0 (d) y" – 2y + 2y = 0 (e) y" + 2y - 8y = 0 (f) y" +9y=0 (g) y" – 4y + 4y = 0 (h) 25y" – 10y' +y=0
(17 points) (a) Find the general solution of the differential equation y" (t) + 36y(t) = 0. general solution = (Use the letters A and B for any constants you have in your solution.) (b) For each of the following initial conditions, find a particular solution. (1) y(0) = 0,7(0) = 1: y= (ii) y(0) = 1, y'(0) = 0: y= (ii) y(0) = 1, y(1) = 0:y= (iv) y(0) = 0, y(1) = 1:y= 1 (On a sheet of...
Q1 (10 points) Consider the differential equation ty" _ y = 0. a) is this differential equation linear? What is its order? Is it homogeneous? b) Try a solution of the form y=x". Is this a solution for some r? If so, find all such r. c) Based on your answer to a) about linearity and b) about what y=x" are solutions, make an educated guess a the general solution looks like. Try that guess and check that it works....
Find a constant k (in terms of a) so that the function fxx (x,y) = e-(x+u) 0 << oo and 0 < y <a and O elsewhere is a valid joint density function.
just focus on A,B,D 1. Homogeneous ODE Find a general solution of the linear non-constant coefficient, homogeneous ODE for y(x) x3y'" – 3xy" + (6 – x2)xy' – (6 – x?)y = 0 as follows. a) You are given that yı(x) = x is a solution to the above homogeneous ODE. Confirm (by substitution) that this is the case. b) Apply reduction of order to find the remaining two solutions, then state the general solution. (Hint: The substitution y2(x) =...
Q1. Consider the equation (a) Find the characteristics of the equation (2). (b) R educe the equation to standard form and find its general solution (c) Use the general solution to find ux, y), if it exists, for each of the following Cauchy data: (iii) u(x,y)-- on the curve 0(2) y n(x,y)-2e-y On the curve 1 x Q1. Consider the equation (a) Find the characteristics of the equation (2). (b) R educe the equation to standard form and find its...
Find the general solution by looking for solutions of the form , where r is a real or complex constant. Use the Equations of EULER-CAUCHY y(t) = + 12" + ty' +y=0,t> 0