Unformatted text preview: y ′′ + y = sin 2 x, y (0) = y (2 π ) , y ′ (0) = y ′ (2 π ) . • Using the ±redholm alternative, determine whether or not this problem has solutions. • If there are solutions, determine them. 4. Consider the following nonhomogeneous boundary value problem: y ′′ + y = f ( x ) , y (0) = y (1) = 0 , where f : [0 , 1] → R is given by f ( x ) = x (1-x ) . Determine a solution of this problem, written as a formal series expansion using an orthonor-mal system of eigenfunctions of the associated homogeneous problem. * MAP 4305; Instructor: Patrick De Leenheer. 1...
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- Summer '06
- Linear Algebra, Boundary value problem, Patrick De Leenheer