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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.)

Respuesta :

Answer:

y =5e^{2x}

Step-by-step explanation:

Given that 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.

Let y =f(x) be the equation of the curve

Since slope = 2y

we have

[tex]\frac{dy}{dx}= 2y\\\\y'     = 2dx\\ln y = 2x+C\\y = Ae^{2x}[/tex]

To find A

It passes through (0,5)

Substitute x=0 and y=5

5=A

SO equation is

[tex]y =5e^{2x}[/tex]

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