IGNOU BMTC 103 2026 - Find the general form of the solution to a linear homogeneous recurren

Question

Find the general form of the solution to a linear homogeneous recurrence relation with constant coefficients for which the characteristic roots are 4, -2 and 3 with multiplicities 2, 1 and 3, respectively. The relation also has a non-homogeneous part which is a linear combination of 3ⁿ and 4ⁿ.

20 Jan 2026

Answer :

Word Count : 303

A linear recurrence relation with constant coefficients is solved by combining the solution of its associated homogeneous relation with a particular solution of the non-homogeneous part. The homogeneous solution is obtained from the characteristic equation, whose roots determine the structure of the general term. When a characteristic root (r) has multiplicity (k), the corresponding contribution to the solution is a polynomial of degree (k-1) in (n) multiplied by (r^n). In this case, the characteristic roots are (4) with multiplicity

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