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Without solving the following differential equations verify if the set of solutions is a vector space a) f"(x) = x; b) x² f" (x) – 2f (x) = 0; c) f'(x) = 2/F(x), x E [0, +∞). Hint: verify if the set of solutions is a vector subspace of the space of all functions

Without solving the following differential equations verify if the set of solutions is a vector space a) f"(x) = x; b) x² f" (x) – 2f (x) = 0; c) f'(x) = 2/F(x), x E [0, +∞). Hint: verify if the set of solutions is a vector subspace of the space of all functions

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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8. Without solving the following differential equations verify if the set of solutions is a vector space a) f"(x) = x; b) x² f"(x) – 2f(x) = 0; c) f'(x) = 2/f(x), x E [0, +∞). Hint: verify if the set of solutions is a vector subspace of the space of all functions
Transcribed Image Text:8. Without solving the following differential equations verify if the set of solutions is a vector space a) f"(x) = x; b) x² f"(x) – 2f(x) = 0; c) f'(x) = 2/f(x), x E [0, +∞). Hint: verify if the set of solutions is a vector subspace of the space of all functions
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