Finding the equation of the curve

Find the equation of the curve in which the subnormal varies as the square of the ordinate.

Find the equation of the curve for which the length of the normal is constant and the curves passes through the point (1,0).

The slope of the tangent to the curve at any point is equal to y + 2x. Find the equation of the curve passing through the origin .

The tangents to a curve at a point on it is perpendicular to the line joining the point with the origin. Find the equation of the curve.

The tangents to a curve at a point on it is perpendicular to the line joining the point with the origin. Find the equation of the curve.

Find the equation of the curve passing through origin and satisfying the differential equation 2xdy = (2x^(2) + x) dx .

Find the equation of the curve passing through (2,1) which has constant sub-tangent.

Find the equation of the curve whose gradient at (x,y) is y/(2x) and which passes through the point (a,2a) .

Find the equation of the curve in which the perpendicular from the origin on any tangent is equal to the abscissa of the point of contact.

Find the equation of the curve which is such that the area of the rectangle constructed on the abscissa of and the initial ordinate of the tangent at this point is a constanta =a^(2)