functional equation

Jul 2011
408
16
If a function \(\displaystyle f\) satisfies the relation \(\displaystyle f(x)f''(x)-f(x)f'(x)=(f'(x))^2\,\forall x \in\mathbb{R}\)

and \(\displaystyle f(0)=f'(0)=1\), then value of \(\displaystyle f(x)\) is .
 
Last edited by a moderator:
Dec 2015
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Earth
\(\displaystyle \displaystyle y = x^{2} +x+1\)
 
Last edited:

skipjack

Forum Staff
Dec 2006
21,473
2,466
That's incorrect.

$f(x) = e^{{\large e^{\large x}} - 1}$
 
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skipjack

Forum Staff
Dec 2006
21,473
2,466
Make the substitution $f(x) = e^{\large v}$, then solving is easy.
 
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