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A curve passes through the point (0, 5) and has the property that the slope of the curve at every point P is twice the y-coordinate of P. What is the equation of the curve? (Use x as the independent variable.) ...?

Verified Answer :

The solution to the problem is as follows:


y' = 2y 

y'/y = 2 

dy/y = 2dx 

lny = 2x + k 

y = (e^k)(e^2x) 

5 = e^k 

y = 5e^(2x)


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