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). Hint: verify if the set of solutions is a vector subspace of the space of all functions

Advanced Engineering Mathematics
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Chapter2: Second-order Linear Odes
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8. Without solving the following differential equations verify if the set of solutions is a
vector space
a) f"(x)
= r; 6) x² f"(x) – 2f(x) = 0; c) f'(x) = 2/f(x).
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) = r; 6) x² f"(x) – 2f(x) = 0; c) f'(x) = 2/f(x). Hint: verify if the set of solutions is a vector subspace of the space of all functions
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