Solve the differential equation (tan−1y−x)dy=(1+y2)dx.
Consider a differential equation of order m and degree n. Which one of the following pairs is not feasible?
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 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
A curve is such that the mid-point of the portion of the tangent intercepted between the point where the tangent is drawn and the point where the tangent meets the y-axis lies on the line y=x˙ If the curve passes through (1,0), then the curve is