At every point on a curve, the slope is the sum of the abscissa and the product of the ordinate and the abscissa, and the curve passes through (0, 1). Find the equation of the curve.

Question

Philoid · Accepted Answer

Given the slope at any time = x + xy

We know that slope of tangent =

∴

⇒

Integrating both sides,

⇒

⇒ ……(1)

Now, the curve passes through (0,1)

So, it must satisfy the above equation

∴

⇒ log 2 = 0 + c

⇒ c = log2

Putting the value of c in equation (1)

∴