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A curve passes through the point (0,7) and has the property that the slope of the curve at every point P is five times the y-coordinate of P. What is the equation of the curve

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Answer:

y(x) = 7e^(5x)

Explanation:

The question says that the slope of the curve at every point P is five times the y-coordinate of P. This means that

dy/dx = 5y

Refer to solutions of differential equations, dy/dt = ky, being in the form of y(t) = y(0) e^(kt)

Using the above stated law now, we can relate to our equation, saying that

y(x) = y(0) e^(5x)

The point given from the question is, (0, 7). This also means that y(0) = 7. So finally, we can have

y(x) = 7e^(5x)

And that is our needed equation of the curve

User Dyachenko
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