Math miscellaneousHard
Question
Let f(x) be differentiable on the interval (0, ∞) such that f(1) = 1, and
for each x > 0. Then f(x) is
for each x > 0. Then f(x) is
Options
A.
B.
C.
D.
Solution
⇒ x2f′(x) - 2xf(x) + 1 = 0
⇒ f(x) = cx2 +
also f(1) = 1⇒ c =
Hence f(x) =
x2 + 
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