Question

1 H grams of artificial sugar in water are being converted into dextrose at a rate which is proportional to the square of the amount unconverted. Find the differential equation expressing the rate of conversion after v minutes given that s grams is converted in v minutes and c being the constant of proportionality.
2 A vehicle of mass m moves along a straight line ( the – axis) while subject to a force indirectly proportional to its displacement x from a fixed point O in its path and 2) a resisting force proportional to its acceleration. Express the total force as a differential equation.
3 Derive the differential equation associated with the primitive
y=Ax^3+Bx^2+Cx+D
where A, B, C and D are arbitrary constants.