Given that a curve is located on the right side of the Y-axis and passes through the point (1.1), the intercept of the tangent at any point on the curve on the y-axis is equal to the abscissa of the tangent point, the curve equation is obtained

Given that a curve is located on the right side of the Y-axis and passes through the point (1.1), the intercept of the tangent at any point on the curve on the y-axis is equal to the abscissa of the tangent point, the curve equation is obtained

Let the curve be y = f (x)
The tangent equation of a curve is y-f (X.) = f '(X.) (X-X.), that is, y = f' (X.) (X-X.) + F (X.)
The problem of X. = - X. f '(X.) + F (X.) can be transformed into the solution of differential equation
The differential equation can be written as x = - XDY / DX + y and dy / DX = Y / X - 1
Let z = Y / x, then y = ZX, dy / DX = Z + XDZ / DX = Y / X-1 = Z-1
XDZ / DX = - 1 separate the two sides of the variable DZ = - DX / X to get z = - LNX + C = Y / X
When y = x (c-lnx) curve passes through the point (1,1) generation, y = x (1-lnx)