38. In many physical applications, the nonhomogeneous term F(x) is speci- fied by different formu...
2. Given the nonhomogeneous 2nd order differential equation y" +2y = xe*: (8 pts) a. Identify the forcing function (ie. the nonhomogeneous term we call f(x)). b. Write the homogeneous equation associated with this DE. c. Find the particular solution to the homogeneous DE from part b which satisfies the initial conditions y(0) = 2, y'(O)=-1. (note: you will NOT be using technique of undetermined coefficients)
All I need answered is C In certain physical models, the nonhomogeneous term, or forcing term, g(t) in the equation ay'' + by' + cy=g(t) may not be continuous, but have a jump discontinuity. If this occurs, a reasonable solution can still be obtained using the following procedure. Consider the following initial value problem. 270 if Osts 7n/6 y'' + 6y' +45y = g(t); y(0) = 0, y' (O) = 0, where g(t) = 0 if t>7n/6 Complete parts (a)...
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...
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. x@y" + xy-y4 - Inxx>0; y(t) = 2, y(t) = 2.y"(1)=5: Yo-Inx-1: {x, xin x, xin x)} (a) Find a general solution to the nonhomogeneous equation yox) - CX+C_x Inx + CyX(In x)2 Inx-1 (b) Find the solution that satisfies the...
a. Find a particular solution to the nonhomogeneous differential equation y" + 16y = cos(4x) + sin(4x). Yo = (xsin(4x))/8-(xcos(4x))/8 help (formulas) b. Find the most general solution to the associated homogeneous differential equation. Use ci and C2 in your answer to denote arbitrary constants. Enter c1 as c1 and C2 as c2. Un = c1cos(4x)+c2sin(4x) help (formulas) c. Find the solution to the original nonhomogeneous differential equation satisfying the initial conditions y(0) = 3 and y'(0) = 2. y...
a. Find a particular solution to the nonhomogeneous differential equation y" + 4y = cos(2x) + sin(2x) b. Find the most general solution to the associated homogeneous differential equation. Use cand in your answer to denote arbitrary constants. c. Find the solution to the original nonhomogeneous differential equation satisfying the initial conditions y(0) = 8 and y'(0) = 4
Find a particular solution to the nonhomogeneous differential equation ?′′+4?′+5?=10?+?−? y ′ ′ + 4 y ′ + 5 y = 10 x + e − x . ??= y p = help (formulas) Find the most general solution to the associated homogeneous differential equation. Use ?1 c 1 and ?2 c 2 in your answer to denote arbitrary constants, and enter them as c1 and c2. ?ℎ= y h = help (formulas) Find the most general solution to the...
Consider the following 2nd order nonhomogeneous linear equation x 00 + 4x 0 + 5x = cos 2t 1. Solve for the fundamental solutions of its associated homogeneous equation. 2. Find a particular solution of the nonhomogeneous equation. 3. Based on your answer to the previous two questions, write down the general solution of the nonhomogeneous equation. Problem II (15 points) Consider the following 2nd order nonhomogeneous linear equation x" + 40' + 5x = cos 2t 1. (6 points)...
Problem 1. Consider the nonhomogeneous heat equation for u(,) subject to the nonhomogeneous boundary conditions 14(0,t) 1, u(r,t)-0,t> and the initial condition the solution u(x, t) by completing each of the following steps (a) Find the equilibrium temperature distribution u ( (b) Denote v, t)t) - u(). Derive the IBVP for the function vz,t). (c) Find v(x, t) (d) Find u(x, t) Problem 1. Consider the nonhomogeneous heat equation for u(,) subject to the nonhomogeneous boundary conditions 14(0,t) 1, u(r,t)-0,t>...
Find the general solution of the following 2nd order linear nonhomogeneous ODEs with constant coefficients. If the initial conditions are given, find the final solution. Apply the Method of Undetermined Coefficients. 7. y" + 5y' + 4y = 10e-3x 8. 10y" + 50y' + 57.6y = cos(x) 9. y" + 3y + 2y = 12x2 10. y" - 9y = 18cos(ix) 11. y" + y' + (? + y = e-x/2sin(1x) 12. y" + 3y = 18x2; y(0) = -3,...