Thread: Problem 24
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Old May 30th, 2007, 08:58 AM
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Originally Posted by ecMathGeek View Post
I would much rather deal with a differential equation. Hopefully this works.

\frac{d}{dx}[f(x)]^2=\frac{d}{dx}\int_0^x [f(t)]^2+[f'(t)]^2dt

2[f(x)]f'(x) = [f(x)]^2+[f'(x)]^2

[f(x)]^2-2 [f(x) \cdot f'(x)] + [f'(x)]^2 = 0

[f(x) - f'(x)]^2=0

f(x)-f'(x)=0
f(x)=f'(x)
f(x) = Ae^x

Am I right?
The LHS is
A^2e^{2x}

and the RHS is
(A^2 - 1)e^{2x}

so I would say "no."

-Dan
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