(a) Verify that y1 x3 and y2 x 3 are linearly independent
Chapter 4, Problem 4.1.39(choose chapter or problem)
(a) Verify that y1 x3 and y2 x 3 are linearly independent solutions of the differential equation x2y 4xy 6y 0 on the interval ( , ). (b) Show that W( y1, y2) 0 for every real number x. Does this result violate Theorem 4.1.3? Explain. (c) Verify that Y1 x3 and Y2 x2 are also linearly independent solutions of the differential equation in part (a) on the interval ( , ). (d) Find a solution of the differential equation satisfying y(0) 0, y(0) 0. 4.2 REDUCTION OF ORDER 129 (e) By the superposition principle, Theorem 4.1.2, both linear combinations y c1y1 c2y2 and Y c1Y1 c2Y2 are solutions of the differential equation. Discuss whether one, both, or neither of the linear combinations is a general solution of the differential equation on the interval ( , ). 40. Is the
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