A curve y = f(x) has the property that the slope of tangent to the curve at every point is reciprocal to the y value of the curve. Write the equation of the curve as a differential equation.

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justaguide | College Teacher | (Level 2) Distinguished Educator

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The curve y = f(x) has the property that the slope of tangent to the curve at every point is reciprocal to the y value of the curve.

The slope of the line tangent to the curve y = f(x) at any point is given by the value of y' = f'(x) at that point. As the slope of the tangent has a value reciprocal to the value of y = f(x), the differential equation is y' = 1/y

The differential equation of the curve is y' = 1/y

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