Given the initial-value problem ?′′ + 3?′ + 2? = 4?, ?(0) = 3, ?′(0) = 1,
Find its homogeneous solution using the Constant Coefficient approach (10pts)
Find is particular solution using the Annihilator method. (10pts)
Find the general solution that satisfies the initial conditions. (5pts)
Given the initial-value problem ?′′ + 3?′ + 2? = 4?, ?(0) = 3, ?′(0) =...
7. Given the initial-value problem y" + 3y' + 2y = 4x2, y(0) = 3, y'0) = 1, a. Find its homogeneous solution using the Constant Coefficient approach (10pts) b. Find is particular solution using the Annihilator method. (10pts) c. Find the general solution that satisfies the initial conditions. (5pts)
Given the non-homogeneous linear system of differential equations ? ′ = −2? − 7? + 3? ?′=−? +4? +?-6t Find its homogeneous solution using the eigenvalue-eigenvector approach (10pts) Use the variation-of-parameters method to find its particular solution (10pts)
I need help (2 points) Consider the initial value problem -,[0 1 y 1 0 -4 2(O) a. Form the complementary solution to the homogeneous equation. b. Construct a particular solution by assuming the orm УР t = a + t and solving or he undetermined constant vectors a and c Form the general solution (t) c(t)(t) and impose the initial condition to obtain the solution of the initial value problem. n(t) y2(t)
Q2 Given the following heat conduction initial-boundary value problem of a thin homogeneous rod, where ?(?,?) represents the temperature. 9??? = ?? ; 0 < ? < 6; ? > 0; B. C. : ?? (0,?) = 0; ?? (6,?) = 0; ? > 0; I. C. : ?(?, 0) = 12 + 5??? ( ? 6 ?) − 4???(2??); 0 < ? < 6 (a) When ? = 0, what would be the temperature at ? = 3? (Use...
Q2 Given the following heat conduction initial-boundary value problem of a thin homogeneous rod, where ?(?,?) represents the temperature. 9??? = ?? ; 0 < ? < 6; ? > 0; B. C. : ?? (0,?) = 0; ?? (6,?) = 0; ? > 0; I. C. : ?(?, 0) = 12 + 5??? ( ? 6 ?) − 4???(2??); 0 < ? < 6 (a) When ? = 0, what would be the temperature at ? = 3? (Use...
Solve the given initial value problem by undetermined coefficients (annihilator approach). el cos(3x) y(3) +9y' y(0) y'(0) = 2 - y"(0) = 1
A particular solution and a fundamental solution set are given for the nonhomgeneous equation below and its corresponding homogeneous equation (a) Find a general solution to the nonhomogeneous equation. (b) Find the solution that satisfies the specified initial conditions xy" + xy - y = 14 - 3 In x. x > 0; (1) - 1. y'(1) -5, y'(1) - - 1; y = 3 in x = 6; 8, 8 P 1, XÃ An xi} (a) Find a general...
Problem 3. Given the initial conditions, y(0) from t- 0 to 4: and y (0 0, solve the following initial-value problem d2 dt Obtain your solution with (a) Euler's method and (b) the fourth-order RK method. In both cases, use a step size of 0.1. Plot both solutions on the same graph along with the exact solution y- cos(3t). Note: show the hand calculations for t-0.1 and 0.2, for remaining work use the MATLAB files provided in the lectures Problem...
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...
Solve the given initial value problem by undetermined coefficients (annihilator approach). Prime not power for (3) y^(3) + 9y' = e^x cos(3x) y(0) = 2 y' (0) = 1 y''(0) = 1