"Published in Newark, California, USA"
Find the equation of a curve whose slope at any point is equal to - (y + 1)/(x + 1) and which passes through the point (0, 0).
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 (x + 1)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(0, 0) to the above equation, we have
Therefore, the equation of a curve is
