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Find the equation of a curve whose slope at any point is equal to y/(y - x) and which passes thru the point (-1, 2).
Solution:
The slope of a curve is equal to the first derivative of a curve with respect to x. In this case, y' = dy/dx. Let's consider the given slope of a curve
Multiply both sides of the equation by (y - x)dx, we have
Integrate on both sides of the equation, we have
In order to get the value of arbitrary constant, substitute the value of the given point which is P(-1, 2) to the above equation, we have
Therefore, the equation of a curve is
