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Tuesday, December 24, 2013

Variable Separation, 4

Category: Differential Equations, Integral Calculus

"Published in Suisun City, California, USA"

Find an equation of a curve that passes thru the point (1, 1) and whose slope at (x, y) is y²/x³.


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