The indicated function y1(x) is a solution of the associated homogeneous equation. Use the method of reduction of order to find a second solution y2(x) of the homogeneous equation and a particular solution yp(x) of the given nonhomogeneous equation. y'' + y' = 1; y1 = 1

Required solution is where A and B are constants.

Step-by-step explanation:

Given nonhomogenous differential equation is,

  with

To find another solution, consider be such that,

Hence,

  where A and B are constants.

Let  

Hence,

where A and B are constants.

which is required solution.

step-by-step explan mxfcg'k; uafwgzfgjhklhgation: