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Differential Equation (Solution known, but I don't understand) 
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#1
Jan1410, 02:25 PM

P: 66

1. The problem statement, all variables and given/known data
In this problem, a function y= g(x) is described. Write a differential equation of the form "dy/dx=f(x,y) having the function g as it's solution (or one of it's solutions). The line tangent to the graph of g at the point (x,y) intersects the xaxis at the point (x/2,0). 2. Relevant equations 3. The attempt at a solution The solution is y'=2y/x. I'm having trouble seeing both why and how. 


#2
Jan1410, 02:34 PM

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P: 25,228

The tangent passes through a point on the curve, call it (x,y) and has a slope y'. That tangent also passes through (x/2,0). Express y' by finding the slope of the line through the two points (x,y) and (x/2,0).



#3
Jan1410, 02:36 PM

P: 66

Thank you so much!



#4
Jan1410, 02:37 PM

P: 665

Differential Equation (Solution known, but I don't understand)
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