Total SolutionThe total solution or the general solution of a nonhomogeneous linear difference equation with constant coefficients is the sum of the homogeneous solution and a particular solution. If no initial conditions are given, obtain n linear equations in n unknowns and solve them, if possible to get total solutions. If y_{(h)} denotes the homogeneous solution of the recurrence relation and y_{(p)} indicates the particular solution of the recurrence relation then, the total solution or the general solution y of the recurrence relation is given by Example: Solve the difference equation Solution: The homogeneous solution of this equation is obtained by putting R.H.S equal to zero i.e., The homogeneous solution is a_{r(h)}= (C_{1}+C_{2} r).2^{r} The equation (i) can be written as (E^{2}4E+4) a_{r}=3r+2^{r} The particular solution is given as
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