Question:
Find the equation of a curve passing through origin if the slope of the tangent to the curve at any point (x, y) is equal to the square of the difference of the abscissa and ordinate of the point.
Solution:
We know that,
The slope of the tangent of the curve = dy/dx
And the difference between the abscissa and ordinate = x – y
So, as given in the question we have
dy/dx = (x – y)2
Taking, x – y = v
