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Find an equation of a curve that passes thru the point (1, 1) and whose slope at (x, y) is y²/x³.
Solution:
The slope of a curve is a first derivative of the equation of a curve with respect to x. In this problem, the slope of a curve at (x, y) is written as
Arrange the above equation by separation of variables, we have
Integrate on both sides of the equation in order to get the equation of a curve as follows
To solve for the value of C, substitute the value of x and y which is the given point in the curve, as follows
Therefore, the equation of the curve is
Multiply both sides of the equation by their Least Common Denominator, which is 2x²y, we have
Therefore, the equation of a curve is
