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Question

The slope of the tangent to the curve at any point is the reciprocal of twice the ordinate at that point. The curve passes through the point (4, 3). Determine its equation.

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Solution

According to the question,
dydx=12y2y dy=dxIntegrating both sides, we get2y dy=dxy2=x+CSince the curve passes throught the point 4, 3, it satisfies the equation of the curve.9=4+CC=5Putting the value of C in the equation of the curve, we gety2=x+5

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