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4. [10] Suppose that the third-order homogeneous linear differential equation ay + by + cy' + dy = 0 has solutions y =ex,y2 =
4. [10] Suppose that the third-order homogeneous linear differential equation ay"" + by" + cy' + dy = 0 has solutions y =ex,y2 = e2x, and y3 = ex. Is S = {y, Y2,Y3} a fundamental solution set for the differential equation? Answer "yes" or "no" and justify your answer.
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