amshearer4719
16.07.2019 •
Mathematics
Acurve passes through the point (0, 3) 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.)
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Ответ:
dy/dx = 2y
and the requirement that y=3 for x=0.
The solution is found as
∫(dy/y) = ∫(2dx)
ln(y) = 2x+c
Substituting the given point gives
ln(3) = 2·0 +c
So the equation can be written as
ln(y) = 2x+ln(3)
or
y = 3e^(2x)
Ответ:
yay thanks
Step-by-step explanation: