Write the differential equation formed from the equation y = mx + c, where m and c are arbitrary constants.

From the differential equation of equation y = a cos 2x + b sin 2x, where a and b are constant.
Find the differential equation representing the family of curves V=Ar+B, where A and B are arbitrary constants.
Form the differential equation of all circles which is tough the x-axis at the origin.
Form the differential equation representing family of curves given by (x – a)² + 2y²= a², where a is an arbitrary constant.
If a unit vector →a makes an angle π3 with ∧i, π4 with ∧j and an acute angle θ with ∧k, then find the value of θ.
The contentment obtained after eating x-units of a new dish at a trial function is given by the function f(x)=x3+6x2+5x+3.. If the marginal contentment is defined as the rate of change of f(x) with respect to the number of units consumed at an instant, then find the marginal contentment when three units of dish are consumed.