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

The differential equation whose solution is A x^2+B y^2=1 , where A and B are arbitrary constants, is of (a) second order and second degree (b) first order and second degree (c) first order and first degree (d) second order and first degree

Find the equation of the curve which passes through the point (4, 3) and the gradient of the tengent to the curve at any point on it is equal to the reciprocal of the ordinate of the point.

The curve for which the length of the normal is equal to the length of the radius vector is/are (a) circles (b) rectangular hyperbola (c) ellipses (d) straight lines

The differential equation of all parabolas each of which has a latus rectum 4a and whose axes are parallel to the x-axis is (a) of order 1 and degree 2 (b) of order 2 and degree 3 (c) of order 2 and degree 1 (d) of order 2 and degree 2

The equation of the curve which is such that the portion of the axis of x cut off between the origin and tangent at any point is proportional to the ordinate of that point is

Find the equation of the curve which is such that the area of the rectangle constructed on the abscissa of any point and the intercept of the tangent at this point on the y-axis is equal to 4.

Which of the following is not the differential equation of family of curves whose tangent form an angle of pi/4 with the hyperbola xy= c^2 ?

The differential equation representing the family of curves y^2=2c(x+sqrt(c)), where c is a positive parameter, is of (A) order 1 (B) order 2 (C) degree 3 (D) degree 4

The order and degree of the differential equation of all tangent lines to the parabola y=x^2 is (a) 1,2 (b) 2,3 (c) 2,1 (d) 1,1

Find the equation of a curve passing through the point (0,1).If the slope of the tangent to the curve at any point (x,y) is equal to the sum of the x coordinate(abscissa) and the product of the x coordinate and y coordinate (ordinate) of that point.