(a) To determine To verify: The given functions are linearly independent and form a basis of solutions of the given ODE. Explanation The given ODE is 4 x 2 y ″ − 3 y = 0 and the basis of the ODE is x 3 2 , and x − 1 2 . Note that, “If y 1 y 2 ≠ constant , then the given functions are linear independent and if y 1 y 2 = constant , then the given functions are linear dependent”. Let y 1 = x 3 2 , and y 2 = x − 1 2 (b) To determine To solve: The given initial value problem and graph or sketch the solution of the ODE.

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ISBN: 9781119096023

Author: Kreyszig

Publisher: WILEY

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Chapter 2.1, Problem 17P

(a)

To determine

To verify: The given functions are linearly independent and form a basis of solutions of the given ODE.

(b)

To determine

To solve: The given initial value problem and graph or sketch the solution of the ODE.

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Chapter 2.1, Problem 16P

Chapter 2.1, Problem 18P

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