大一高数两道题
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1）F(x) = xf(x)
F(0) = 0
F(1) = 0
F'(x) = f(x) + xf'(x)
必有一点F'(e) = f(e)+ef'(e) = 0
f'(e) = -f(e)/e
2)
dy/dx = y
=>dy/y = dx
=>lny = x+C
=>y=e^(x+C)
f(0) = e^c = 1 =>C=0
=>y = e^x
F(0) = 0
F(1) = 0
F'(x) = f(x) + xf'(x)
必有一点F'(e) = f(e)+ef'(e) = 0
f'(e) = -f(e)/e
2)
dy/dx = y
=>dy/y = dx
=>lny = x+C
=>y=e^(x+C)
f(0) = e^c = 1 =>C=0
=>y = e^x
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