General solution of non-homogenous 2nd order linear differential equations : d²y/dx² - 4y = e^(3x)

Please find the general solution of the nonhomogenous second order linear differential equation below by following these steps: 1. Find the general solution y= C1y1 + C2y2 of the associated homogenous equation (complementary solution) 2. Find a single solution of yp of above.(particular solution). 3. Express the general so ...continues

General solution of non-homogenous second order linear differential equations : d²y/dx² + y = cosx

Please find the general solution of the nonhomogenous second order linear differential equation below by following these steps: 1. Find the general solution y= C1y1 + C2y2 of the associated homogenous equation (complementary solution) 2. Find a single solution of yp of above.(particular solution). 3. Express the general so ...continues

IVP : Solve a linear differential equation : dy/dx + xy = x y(0) = -6

Solve the initial value problem below. the initial condition is y(0) = -6 The differential equation is dy/dx + xy = x Please show all details in the solution, including the steps to find the value of C. thank you!

General solution to nonhomogenous second order differential equation : d²y/dt² - 9y = sint

Please find the General solution to the non-homogenous second order differential equation below. Please show all details in your solution. Thank you d²y/dt² - 9y = sint

Particular solution of differential equation : d²y/dx² - y = xe^x

The differential equation is: d²y/dx² - y = xe^x For the first part of the general solution, I got y=Ae^x + Be^-x where a and b are constants. Now I need to find the particular solution. Thanks.

General solution to nonhomogenous second order linear differential equations : d²y/dx² + 5dy/dx - 6y = 7e^x

Find the general solution of the nonhomogenous second order linear differential equation below. Please show detailed solution steps. Thanks, d²y/dx² + 5dy/dx - 6y = 7e^x

General solution to a nonhomogenous second order linear differential equation : d²y/dx² + 6dy/dx + 9y = e^(-4x)

Please find the general solution of the nonhomogenous second order linear differential equation below. Please show all details in the solution. Thanks d²y/dx² + 6dy/dx + 9y = e^(-4x)

Differential Equations and Green's Functions

Consider the inhomogeneous differential equation -u’ + u = r(x) on (a,b) where r(x) is a continuous function on the interval (a,b) Find the solution to this differential equation in the form u = integral from a to b (G(x,s) r(s) ds) and determine G(x,s).

Particular solution for nonhomogenous second order linear differential equation : d²y/dt² - 9y = sint

I have already found the first part of the general solution for the equation below, but am not sure how to find the particular solution for the sint part of the equation. Please find the particular solution for sin t in this problem and show all details. d²y/dt² - 9y = sint

Particular solution for non-homogogenous second order linear differential equation : d²y/dx² + y = cosx

Please find the particular solution for cosx in this problem and show all details. d²y/dx² + y = cosx