The slope of a curve art each of its points is equal to the square of the abscissa of the point. Find the particular curve through the point (-1,1).

If the slope of the tangent is equal to the square of tha abscissa of the point on the curve, then the differential equation is

The curve whose subnormal w.r.t any point is equal to the abscissa of that point is a

The perpendicular from the origin to the tangent at any point on a curve is equal to the abscissa of the point of contact.Also curve passes through the point (1,1). Then the length of intercept of the curve on the x-axis is

Find the equation of the curve passing through origin if the slope of the tangent to the cuurve at any point (x,y) is equal to the square of the difference of the abscissa and ordinate of the point.

The curve in which the slope of the tangent at any point equal the ratio of the abscissa to the ordinate of the point is

At any point on a curve , the slope of the tangent is equal to the sum of abscissa and the product of ordinate and abscissa of that point.If the curve passes through (0,1), then the equation of the curve is

The x-intercept of the tangent to a curve is equal to the ordinate of the point of contact. The equation of the curve through the point (1,1) is