e differential equation y 0 + y = 1 2−x with the initial conditions y(0) = 2. We wish to approximate y(1) using another method.
please help me, thanks so much
e differential equation y 0 + y = 1 2−x with the initial conditions y(0) =...
Please teach me this.. Consider the same differential equation y' +y= with the initial conditions y(0) = 2. We wish to approximate y(1) using another method. (a) Use the method of series to by hand to find the recursion relation that defines y(t) = {mo anx" as a solution to this differential equation. (b) Let Pn(x) = EX=anx" be the Nth degree polynomial that approximates y(x). Use Mathematica to calculate P4(1), P16(1), P64(1), and P256 (1).
= 2. We wish to 7. Consider the differential equation y' + y = 2.. with the initial conditions y(0) approximate y(1). (a) Set up Euler's method by hand and use it to approximate y(1) with a step size of h = 25. (You may use only a calculator for this question) (b) Use Mathematica to do Euler's method with the step sizes of h= .1,.01, .001, and .0001.
The differential equation : dy/dx = 2x -3y , has the initial conditions that y = 2 , at x = 0 Obtain a numerical solution for the differential equation, correct to 6 decimal place , using , The Euler-Cauchy method The Runge-Kutta method in the range x = 0 (0.2) 1.0
Solve the next differential equation with initial conditions y(0) = 1 and y'(0) = 1 by reducing it in order −24y′ y′′ = −16y OPTIONS y= (1 3 y= (1+3) y = (1 + x) y (1 r) alic y= (1 3 y= (1+3) y = (1 + x) y (1 r) alic
Find the solution of the differential equation according to the initial conditions of y (0) = 0, y '(0) = 1 2) y" + 3 y'= 1 - 9x? diferansiyel denkleminin Y(0)=0, y'(0) = 1 başlangia kosullarini sağlayan çözümünü bulunuz. (15 p.) ini
(1 point) a. Consider the differential equation: d2y 0.16y-0 dt2 with initial conditions dt (0)-3 y(0)--1 and Find the solution to this initial value problem b. Assume the same second order differential equation as Part a. However, consider it is subject to the following boundary conditions: y(0)-2 and y(3)-7 Find the solution to this boundary value problem. If there is no solution, then write NO SOLUTION. If there are infinitely many solutions, then use C as your arbitrary constant (e.g....
(1 point) In this problem you will solve the differential equation (+7)y"+11xy' - y=0. x" for the differential equation will converge at least on the interval (-inf.-sqrt(7)] (1) Ey analyzing the singular paints of the differential equation, we know that a series solution of the form y = . (2) Substituting y = . *" into (x2+7y" + 11xy - y = 0, you get that Multiplying the coefficients in x through the sums E Reindex the sums Finally combine...
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...
7. Consider the differential equation (a) Show that z 0 is a regular singular point of the above differential equation (b) Let y(x) be a solution of the differential equation, where r R and the series converges for any E (-8,s), s > 0 Substitute the series solution y in to the differential equation and simplify the terms to obtain an expression of the form 1-1 where f(r) is a polynomial of degree 2. (c) Determine the values of r....
Solve the differential equation below with initial conditions. . Find the recurrence relation and compute the first 6 coefficients (a -a,) (1 3x)y y' 2xy 0 y(0) 1, y'(0)-0