Find the solution of the initial value problem [y(0)=-1, у"(0)=-3, у "(0)=0, у"(0)-0] a) y--3-х -2x-2x...
Consider the following initial value problem у(0) — 0. у%3D х+ у, (i) Solve the differential equation above in tabular form with h= 0.2 to approximate the solution at x=1 by using Euler's method. Give your answer accurate to 4 decimal places. Given the exact solution of the differential equation above is y= e-x-1. Calculate (ii) all the error and percentage of relative error between the exact and the approximate y values for each of values in (i) 0.2 0.4...
Given a second order linear homogeneous differential equation а2(х)у" + а (х)У + аo(х)у — 0 we know that a fundamental set for this ODE consists of a pair linearly independent solutions yı, V2. But there are times when only one function, call it y, is available and we would like to find a second linearly independent solution. We can find y2 using the method of reduction of order. First, under the necessary assumption the a2(x) F 0 we rewrite...
2. Given two initial value problems, у" — р(г)у +q()у +r(x) with a <I<b,y(a) — с,1 (а) —0 (1) and у" — р(г)у + g(х)у with a < r <ь,y(a) — 0, and / (а) — 1 (2) [a, b) where p(x), q(z) and r(x) Show that given two solutions yı(x), y2(x) to the linear value problems above, (1) and (2), respectively, then there exists a solution y(x) to a linear boundary value problem above where y(a) %3D 0, у...
Find the solution of the given initial value problem: y(4) + 2y" + y y(3) (0) y, (0) 0, y', (0) llt + 2; y (0) 1 Enclose arguments of functions in parentheses. For example, sin (2x) Find the solution of the given initial value problem: y(4) + 2y" + y y(3) (0) y, (0) 0, y', (0) llt + 2; y (0) 1 Enclose arguments of functions in parentheses. For example, sin (2x)
Find the solution of the given initial value problem: y" + y = f(t); y(0) = 6, y'(0) = 3 where f(t) = 1, 0<t<3 0, įst<<
Find the solution to the problem with the following initial value: We ask for an explicit solution. Justify each step of your solution. Indication: where A and B are constants. с22 dy 1 — 0, х > 0, у(0) — 1. у(1 + 2) х dx В и = A + 1 u 1u
(1 point) Solve the given initial value problem y′=2+e^(y−2x+4 ) y(0)=−4 The solution in the implicit form is F(x,y)=1, where F(x,y)= ? i had answer of this {y-ln(1/(-x+1))-2x+5}, don't know why its wrong.
Find the solution y of the initial value problem 3"(t) = 2 (3(t). y(1) = 0, y' (1) = 1. +3 g(t) = M Solve the initial value problem g(t) g” (t) + 50g (+)? = 0, y(0) = 1, y'(0) = 7. g(t) = Σ Use the reduction order method to find a second solution ya to the differential equation ty" + 12ty' +28 y = 0. knowing that the function yı(t) = + 4 is solution to that...
Consider the initial value problem for function y, y" – ' - 20 y=0, y(0) = 2, 7(0) = -4. a. (4/10) Find the Laplace Transform of the solution, Y(8) = L[y(t)]. Y(8) = M b. (6/10) Find the function y solution of the initial value problem above, g(t) = M Consider the initial value problem for function y, Y" – 8y' + 25 y=0, y(0) = 5, y(0) 3. a. (4/10) Find the Laplace Transform of the solution. Y(s)...
Can someone explain how to do this problem? 2. Let f(t, y) — х +у, 0<x< 1, 0 <y<1 < ,Y < !) (a) Find P (X 1 2 (b) Find P(X < 2Y)