Abscissa means the x-coordinate and ordinate means the y-coordinate

Slope of tangent is given as square of the difference of the abscissa and ordinate

Difference of abscissa and ordinate is (x – y) and its square will be (x – y)²

Hence slope of tangent is (x – y)²

Slope of tangent of a curve y = f(x) is given by

Substitute x – y = z hence y = x – z

Differentiate x – z with respect to x

Using partial fraction for

Equating numerator

⇒ A(1 – z) + B(1 + z) = 1

Put z = 1

⇒ B = 1/2

Put z = -1

⇒ A = 1/2

Hence

Put in (a)

Integrate

⇒ x = 1/2(log(1 + z) + (–log(1 – z)) + c

⇒ 2x = log(1 + z) – log(1 – z) + c

Using log a – log b = log

Resubstitute z = x – y

Now it is given that the curve is passing through origin that is (0, 0)

Hence (0, 0) will satisfy the curve equation (b)

Putting values x = 0 and y = 0 in (b)

⇒ c = 0

Put c = 0 back in equation (b)

⇒ e^2x(1 – x + y) = (1 + x – y)

Hence equation of curve is e^2x(1 – x + y) = (1 + x – y)