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 Differential Equations Ordinary and Partial Differential Equations Math Forum

November 22nd, 2016, 03:06 PM   #1
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Help read the graph, the formula model is in the picture.
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 November 22nd, 2016, 05:03 PM #2 Math Team   Joined: Jan 2015 From: Alabama Posts: 2,579 Thanks: 668 What do you mean by "read the graph"- what do you want to learn from the graph? And why was this posted under "differential equations"?
 November 22nd, 2016, 07:44 PM #3 Global Moderator   Joined: Dec 2006 Posts: 17,729 Thanks: 1360 Presumably, "read the graph" means that the values of the four constants in the given equation are to be estimated by inspection of the graph. For example, the equation implies f(0) = B. As the graph shows that f(0) = 1, one can conclude that B = 1. I would suggest that $\beta= 6\pi$.
November 23rd, 2016, 03:06 AM   #4
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Quote:
 Originally Posted by Country Boy What do you mean by "read the graph"- what do you want to learn from the graph? And why was this posted under "differential equations"?
By reading the graph, I meant to find α,β,A,B, for y(x)=e^(αx)(Asin(βx)+Bcos(βx)).

And that equation is differential equations of second order with 2 complex roots.

Last edited by skipjack; February 7th, 2017 at 04:17 PM.

 November 23rd, 2016, 04:52 AM #5 Global Moderator   Joined: Dec 2006 Posts: 17,729 Thanks: 1360 If you accept my suggestions that B = 1 and $\beta$ = 6$\pi$, I would further suggest that A = tan(2$\pi$/5). These values of A and $\beta$ are based on assumptions about the exact values of $x$ where the graph's turning points occur. Unfortunately, one can't be so precise in giving the value of $\alpha$, because the graph depicts the function using a rather broad line.

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