Question
Find the equation of a curve passing through the origin given that the slope of the tangent to the curve at any point (x, y) is equal to the sum of the coordinates of the point.
Solution
Let y = f (x) be the equation of curve.
We know that
represents the slope of the tangent to the curve at the point (x, y).
From the given condition.
or 
Comparing
Solution of differential equation is
or
or
or
or
or
...(1)
Now curve passes through origin (0, 0).
from (1), 
is the required equation of curve.
We know that
represents the slope of the tangent to the curve at the point (x, y).From the given condition.
or Comparing
Solution of differential equation is
or
or
or
or
or
...(1)Now curve passes through origin (0, 0).
from (1), is the required equation of curve.
