need answers to both! 16. [-/1 Points] DETAILS ZILLDIFFEQMODAP116.4.002. Use (1) in Section 6.4. x2y" +...
First use (20) in Section 6.4. y'' + 1 − 2a x y' + b2c2x2c − 2 + a2 − p2c2 x2 y = 0, p ≥ 0 (20) Express the general solution of the given differential equation in terms of Bessel functions. Then use (26) and (27) J1/2(x) = 2 πx sin(x) (26) J−1/2(x) = 2 πx cos(x) (27) to express the general solution in terms of elementary functions. (The definitions of various Bessel functions are given here.) y''...
Section: 003 402 404 406 3) Bessel's Functions. Consider the differential equation x2y" +xy +xy-o. a) Use the method of Frobenius (which we learned in 7.3) to find a recurrence relation for the power series solution of xy"+xy'+y-o b) Find a general form of the answer, using only factorials (not the Gamma function). c) Determine the radius of convergence of your power series answer. d) This is called a Bessel function of order zero. What is the differential equation for...
[-/1.25 Points] DETAILS ZILLDIFFEQMODAP11 4.2.007. The indicated function y(x) is a solution of the given differential equation. Use reduction of order or formula (5) in Section 4.2, e-P(x) dx r2 = y g(x) / dx (5) as instructed, to find a second solution v2(X). Ay" - 20y + 25y = 0; Y-S/2 Y2 Need Help?
Differential Equations MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER [0/1 Points) DETAILS PREVIOUS ANSWERS ZILLDIFFEQMODAP11 1.2.007. In this problem, x=, cost+c, sint is a two-parameter family of solutions of the second-order DEX" + x -0. Find a solution of the second-order IVP consisting of this differential equation and the given initial conditions. x(0) --1, x(0) = 3 X=0 X
Section 6.4 Discontinuous Forcing Functions: Problem 1 Previous Problem Problem List Next Problem Results for this submission Entered Answer Preview Result 5-5 exp(-28) +4s s2 +64 [55"exp(-2%)+4*S)/[(s*2)-64] incorrect The answer above is NOT correct. (1 point) Consider the following initial value problem: 5, 0t2 (0)4, (0) 0 0, t> 2 Using Y for the Laplace transform of y(t), ie., Y- Ly(t). find the equation you get by taking the Laplace transform of the differential equation and solve for 8 (5-5exp(-2s)+4s/(S...
6. [0/2 points) DETAILS PREVIOUS ANSWERS Find the general (real) solution of the differential equation: y"- 2y'- 15y=-51 sin(3 x) -3x | Ae 5x + Be 34 y(x) = 8.5 + -cos(3x) * 17 51 14 sin(3x) - - Find the unique solution that satisfies the initial conditions: Y(0) = 2.5 and y'(o)=37 y(x) = 7. [-12 Points) DETAILS Find the general (real) solution of the differential equation: y" + 4y' + 4y=64 cos(2x) y(x) = Find the unique solution...
[0/1 Points] DETAILS PREVIOUS ANSWERS LARCAL Find the differential dy of the given function. (Use "dx" for dx.) x + 2 y = 4x - 5 dy Need Help? Read It Talk to a Tutor Submit Answer [-/1 Points] DETAILS LARCALC11 3.9.027. Find the differential du fithe nimen function useil dx" for dx.)
. [1/4 Points] DETAILS PREVIOUS ANSWERS ROLFFM8 2.3.022. MY The matrix given is in reduced echelon form. 1 02 -4 0 1 5 2 0 0 0 0 Write the system of equations represented by the matrix. (Use x as your variable and label each x with its corresponding column. Enter x_1 for xy, X2 row 1 x + 2y = -4 X row 2 x + 5y TOW 3 0 0 Find the solution, if possible. (If there are...
prove that J2(x)=sum from k=0 to infinity [ (-1)^k/2^9@k+2)*k!(k+2)! ]*x^(2k+2) is a solution of the Bessel differential equation of order 2: x^2y'' + xy' + (x^2-4)y=0 (-1)4 9- Using the ratio test, one can easily show that the series +2converges for all e R. Prove that (-1)X h(x) = E, 22k +2k!(k + 2)! 22+2 is a solution of the Bessel differential equation of order 2: In(x) is called the Bessel function of the first Remark. In general the function...
I need to answer a, c, and d 1. Find the limit at xo if it exists. (a) f(x, y) = xy/(x2 + y2), Xo = el + e2 (b) f(x, y) = xy/(x2 + y2), Xo = (0,0). (c) f(x) = (1-cos x)/x2, X,-0. [Hint: limx-o (sin x)/x = 1 .] (d) f(x)-|x-2le, + lx + 2le_, xo = 3. (e) f(x, y) = ye, + (xy)리[(xy)2 + (x-y)2je2, Xo = (0,0). At which points is each of these...