Practice Prelim 2 Solution 1 - 1. Find a linear...

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Unformatted text preview: 1. Find a linear differential operator L so that one solution of the differential equation Ly = 0 is: y(x) = 10xex + x3 ex - 2 sin(3x)ex + 10 Solution: The differential operator (D - 1)4 sends Ax3 ex + Bx2 ex + Cxex + D to zero. The differential operator ((D - 1)2 + 32 ) sends A sin(3x)ex + B cos(3x)ex to zero. The differential operator D sends A to zero. So the composition of these three operators will send y to zero. L = (D - 1)4 (D - 1)2 + 32 D Ly = 0 1 ...
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