2.3 Yk+1- Yk = (n+1)k" The linear inhomogeneous difference equation Yk+1 – Yk = (n + 1)k" (2.48) %3D FIRST-ORDER DIFFERENCE EQUATIONS 51 can be written as Ayk = (n + 1)k", (2.49) %3D where n is an integer. Consider the following equations and associated solutions: Ayk = 0, Yk = A; (2.50) Ayk = 1, Yk = k+ A; (2.51) Ayk = 2k, Yk = k² – k + A; (2.52) Ayk = 3k², yk = k³ – 3/½ k² + /½k + A; (2.53) %3D etc. In each case, A is an arbitrary constant. For n arbitrary, we have k-1 Yk = (n + 1)A-'(k") = (n + 1) i" + A, (2.54) i=1

2.3 Yk+1- Yk = (n+1)k" The linear inhomogeneous difference equation Yk+1 – Yk = (n + 1)k" (2.48) %3D FIRST-ORDER DIFFERENCE EQUATIONS 51 can be written as Ayk = (n + 1)k", (2.49) %3D where n is an integer. Consider the following equations and associated solutions: Ayk = 0, Yk = A; (2.50) Ayk = 1, Yk = k+ A; (2.51) Ayk = 2k, Yk = k² – k + A; (2.52) Ayk = 3k², yk = k³ – 3/½ k² + /½k + A; (2.53) %3D etc. In each case, A is an arbitrary constant. For n arbitrary, we have k-1 Yk = (n + 1)A-'(k") = (n + 1) i" + A, (2.54) i=1

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Description: Explain the determaine red 2.3 Yk+1 - Yk = (n+ 1)k"The linear inhomogeneous difference equationYk+1 – Yk(n + 1)k"(2.48)FIRST-ORDER DIFFERENCE EQUATIONS51can be written asAyk = (n + 1)k",(2.49)where n is an integer.Consider the following equations and

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Chapter2: Second-order Linear Odes

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Explain the determaine red

2.3 Yk+1 - Yk = (n+ 1)k"
The linear inhomogeneous difference equation
Yk+1 – Yk
(n + 1)k"
(2.48)
FIRST-ORDER DIFFERENCE EQUATIONS
51
can be written as
Ayk = (n + 1)k",
(2.49)
where n is an integer.
Consider the following equations and associated solutions:
Ayk = 0, Yk = A;
(2.50)
%3D
Ayk = 1, Yk = k + A;
(2.51)
Ayk = 2k, Yk = k² – k + A;
Ayk = 3k2, Yk = k³ – 3/½ k² + /½ k + A;
(2.52)
(2.53)
etc.
In each case, A is an arbitrary constant. For n arbitrary, we have
k-1
Yk = (n+ 1)A¬'(k") = (n + 1) i" + A,
(2.54)
%3D
i=1

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