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Guessing functions given initial conditions 
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#1
Nov2211, 10:38 PM

P: 3

Is there any way to mathematically derive functions that satisfy a given set of initial conditions? I know this sounds very general, but say for:
f(1)f(0)=0 and f'(1)=1 I've resolved myself to guessing and checking. I've found a function for the opposite: e*texp(t)  ([e*1  exp(1)]  [e*0  exp(0)] = [0][1]= 1  derivative is e  exp(t) > (e  exp(1) = 0) but given how long it took just to guess that function, I was hoping for a more concrete way to find these functions. 


#2
Nov2211, 10:59 PM

P: 3

Of course after posting this, I come up with a very simplistic solution...x^2  x. But, had to guess...so still doesn't solve the problem for me.



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