Explain the deretmine blue or solve the Q(D) 5.5.4 Example DLet us investigate the case where the inhomogeneous term contains a factorthat also appears in the solution of the homogeneous equation. Consider thefirst-order equation(aE1 + bE2 + c)z(k, l) = F(k,l),(5.183)where a, b, and c are constants, and F(k, l) satisfies the condition(aE1 + bE2 + c)F(k, l) = 0.(5.184)188Difference EquationsIf we assume that the particular solution has the formZp(k, l) = (Ak + Bl)F(k, l),(5.185)where A and B are unknown constants, then substitution of this result intoequation (5.183) gives(AAE1 + 6BE2 – 1)F(k, l) = 0.(5.186)%3D|Comparison of equations (5.184) and (5.186) allows the conclusionA = B = -1/c.(5.187)Therefore, for this case, the particular solution isžp(k, l) = (-1/c)(k + l)F(k, l).(5.188)

Name: Explain the deretmine blue or solve the Q(D) 5.5.4 Example DLet us inv
Uploaded: 2024-03-20T07:07:12.000Z
Channel: Bartleby
Description: Explain the deretmine blue or solve the Q(D) 5.5.4 Example DLet us investigate the case where the inhomogeneous term contains a factorthat also appears in the solution of the homogeneous equation. Consider thefirst-order equation(aE1 + bE2 + c)z(k, l