4. Find the Wronskian for y1 = x , y2 = cos(2x), and y3 = e . 4. (10 points) Find the Wronskian for yı = 23, y2 = cos(2x), and y3 = e3r.
10. In solving by variation of parameters, you must find the Wronskian, W. Find W for the differential equation y*-y-2y=e' lx You do not have to solve the differential equation. (a) W = 4 (b) w=1621 12 2 (c)w= (d) w =-6e (e) W = 4* +6xe (f) w = (g) w =-3e (h) w -2,1 8 2 te-2 11. Use the method of variation of parameters to find the solution to y"+3y' + 2 y = 4e (a) y,...
l.a. FIND F SUCH THAT F= vf IF F = (2xY-2, x+22, 24-2X=) b. FIND THE WORK DONE UNDER IN MOVING A BODY PROM (-3,-2-D TO (1,2,3)
Given: y''+2y'=2x+5-e^-2x General solution is: y=c1e^-2x+c2 +1/2(x^2)+2x+1/2(xe^-2x) Solve using the method of undetermined coefficients and show all steps please! I have the form of yp is Ax^2+Bx+Cxe^-2x, and the issue that plagues me is in solving for A B C. I get A=1/2 and I get B=2, but the terms involving C fall off the face of the earth when I substitute y' and y'' of the solution form into the equation, so how can I solve for C? Help...
Find the Wronskian of the given functions and determine if the functions are independent or linearly dependant linearly y1yx+3 y =2x-5
Problem 25 please -Sesin(2x)-9ecos(2x). 21. W = Span(B), where Br(x2e-4x , xe®, e-4x); f(x)--5x2r" + 2e-4-1e 22. W= Span(B),where B= ({x25, x5*, 5x)); f(x)--4x2 5x+9s5x-2(5x). 3 W Span(B), where B (Exsin(2x), xcos(2x), sin(2x), cos(2x)y): f(x) = 4x sin(2x) + 9x cos(20-5 sin(2x) + 8 cos(2x). 24, In Exercise 21 of Section 3.6, we constructed the matrix [D, of the derivative operator D on W- Span(B), where B e sin(bx), e" cos(bx)): Dls a a. Find [D 1g and [D'lg: Observe...
Need help with this wronskian problem y1(x)=e^(x) * cosx & y2(x)=e^(x) * sinx Find the values of the wronskian y1,y2 Determine if the solutions are linearly independent
step by step please Without the aid of the Wronskian, determine whether the given set of functions is linearly independent or linearly dependent on the indicated interval. (a) (%) = In x, f(x) = Inx",(0, ) linearly dependent linearly independent (b) (x) = 2x",,(*) - +, n = 1, 2, Vdots, (-,) linearly dependent linearly independent (c) (X) = x, f(x) - X+4.(-.,-) linearly dependent linearly independent ,) (d) {(x) = cos(x + 2), f(x) - sinx, ( linearly dependent...
Find the Wronskians of the following sets of functions and statewhat that Wronskian implies aboutlinear independence or dependence of the set.(5) 2x + 11; 22x + 121 on (-∞,∞)(6) sin(x); sin(2x) on (-∞,∞)(7) x2 + x - 2; x2 + x; x2 + x - 6on (-∞,∞)(8) x2 + x - 2; x2 + x + 1; x2 + x- 5 on (-∞,∞)
(1 point) It can be shown that yı = e-4x and y2 = xe-4x are solutions to the differential equation y + 8y +16y=0 on the interval (-00, 00). Find the Wronskian of yn y (Note the order matters) W(y1, y2) = Do the functions yn y form a fundamental set on (-00,00)? Answer should be yes or no