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Linear Differential Equations: Variation of Parameters or Reduction of Order?
 

Summary: Linear Differential Equations: Variation of
Parameters or Reduction of Order?
Douglas R. Anderson
Concordia College, Moorhead, Minnesota
7:30 pm, 28 October 2011, Science Lab 104
Ordinary Differential Equations
y (t) + p(t)y (t) + q(t)y(t) = r(t), t R
Recall that by using Lagrange's variation of parameters method the
above linear second-order ODE has solutions of the form
y = c1y1 + c2y2 + yd ,
where y1, y2 are linearly independent solutions of
y (t) + p(t)y (t) + q(t)y(t) = 0. Here
yd (t) = y2(t)
t
a
y1(s)r(s)
W (y1, y2)(s)
ds - y1(t)
t
a

  

Source: Anderson, Douglas R. - Department of Mathematics and Computer Science, Concordia College

 

Collections: Mathematics