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

For the equation of the curve whose subnormal is constant then,

The equation of the curve whose subnormal is constant is

The equation of the curve whose subnormal is twice the abscissa, is

Prove that for the curve y=be^(x//a) , the subtangent is of constant length and the sub-normal varies as the square of the ordinate .

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 .

Find the equation of the circle which lies in the first quadrant and touching each-co ordinate-axis at a distance of 2 units from the origin.

If the length of the portion of the normal intercepted between a curve and the x-axis varies as the square of the ordinate, find the equation of the curve.

The differential equation of the curve for which the initial ordinate of any tangent is equal to the corresponding subnormal (a) is linear (b) is homogeneous of second degree (c) has separable variables (d) is of second order

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

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