Orange Coast College: Math A285 Differential Equations 4.2: Reduction of Order

Math A285
Di↵erential Equations §4.2: Reduction of Order


Instructor: Scott Northrup




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, Reduction of Order



Consider a homogeneous linear second order di↵erential equation

a2 (x)y 00 + a1 (x)y 0 + a0 (x)y = 0

We seek two linearly independent solutions to this equation. If y1
and y2 are linearly independent, then u(x) = y2 (x)/y1 (x) is
non-constant.
Given a single solution y1 (x), we attempt to find y2 (x) by plugging
y2 (x) = u(x)y1 (x) into the equation to determine u(x). We call
this method reduction of order.




This study source was downloaded by 100000900706475 from CourseHero.com on


10-07-2025 23:32:38 GMT -05:00


https://www.coursehero.com/file/251467105/42pdf/