The difference equation 5y% – 6yk + 2 6y – 8yk + 3 - Yk+1 = has two fixed points at (5,) and (1, 1). Calculate asymptotic expan- sions to the solution about these points. Show that the exact solution to this difference equation is 1+c2* Yk = 2+ c2* > c= constant.

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Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.