Question
Find the equation of a curve passing through the point (0, 1). If the slope of the tangent to the curve at any point (x, y) is equal to the sum of x coordinate (abscissa) and the product of the x coordinate and y coordinate (ordinate) of that point.
Solution
Let y = f (x) be equation of curve.
Now
is the slope of the tangent to the curve at point (x, y)
From the given condition,
or 
Comparing
with 
we get, P = -x, Q = x
Solution of differential equation is
or
...(1)
Let
Put
or
...(2)
Since the curve passes through (0, 1)
from (2), 
or
, which is required equation of curve.
Now
is the slope of the tangent to the curve at point (x, y)From the given condition,
or Comparing
with we get, P = -x, Q = xSolution of differential equation is
or
...(1)Let
Put
or
...(2)Since the curve passes through (0, 1)
from (2), or
, which is required equation of curve. 
