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Consider the differential equation x³y + 12x²y" + 25xy' - 25y = 0; x, x5, x-5 5 In(x), (0, 00). Verify that the given functions form a fundamental set of solutions of the differential equation on the indicated interval. In(x)) = -5 The functions satisfy the differential equation and are linearly independent since W(x, x² , X #0 for 0 < x < 00.

Consider the differential equation x³y + 12x²y" + 25xy' - 25y = 0; x, x5, x-5 5 In(x), (0, 00). Verify that the given functions form a fundamental set of solutions of the differential equation on the indicated interval. In(x)) = -5 The functions satisfy the differential equation and are linearly independent since W(x, x² , X #0 for 0 < x < 00.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Consider the differential equation x³y"" + 12x²y" + 25xy' - 25y = 0; x, x5, x-5 In(x), (0, 00). Verify that the given functions form a fundamental set of solutions of the differential equation on the indicated interval. In(x)) = -5 The functions satisfy the differential equation and are linearly independent since W(x, x² , X #0 for 0 < x < 00.
Transcribed Image Text:Consider the differential equation x³y"" + 12x²y" + 25xy' - 25y = 0; x, x5, x-5 In(x), (0, 00). Verify that the given functions form a fundamental set of solutions of the differential equation on the indicated interval. In(x)) = -5 The functions satisfy the differential equation and are linearly independent since W(x, x² , X #0 for 0 < x < 00.
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