Answer to Question #59053 in Differential Equations for ABJ

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.
(a)ds/dv = c(H−s)2
(b) ds/dv = c(H−s)^2
© ds/dv/= (s−H)^2
(d) dv/ds/= c(H−s)
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.

(a) 7md^2/xdt^2=k1/t − k2dx/dt
(b) Md^2x/dt^2=−k1/t−k2d^2x/dt^2
© m d^2x/dt^2=−k1/x−k2d^2x/dt^2
(d) M d^−2x/dt^2=−2 k1/x − k2 d^2x/dt^2