Solve the following differential equation :
(1 + x²) dy + 2xy dx = cot x dx, (x ≠ 0)
Find the general solution of the differential equation (1 + tan y)(dx – dy) + 2xdy = 0.
Form the differential equation representing family of curves given by (x – a)² + 2y²= a², where a is an arbitrary constant.
Find the equation of tangent to the curve 4x² + 9y² = 36 at the point (3 cos θ, 2 sin ).
The total cost associated with provision of free mid-day meals to x students of a school in primary classes is given by C(x) = 0·005x³ – 0·02x² + 30x + 50. If the marginal cost is given by rate of change of total cost, write the marginal cost of food for 300 students.
If the function f : R → R is given by f(x) = x² + 3x + 1 and g : R → R is given by g(x) = 2x – 3, then find
(i) fog (ii) gof
Find the general solution of the differential equation (1 + tan y)(dx – dy) + 2xdy = 0.
Find the equation(s) of the tangent(s) to the curve y = (x³ – 1) (x – 2) points where the curve intersects the x-axis.