Differential equation [Essential - Review question]

[kevinn_h]

Two chemicals, A and B, are put together in a solution where they react to form a compound,
X. The rate of increase of the mass, x kg, of X is proportional to the product of the masses of
unreacted A and B present at time t minutes. It takes 1 kg of A and 3 kg of B to form 4 kg of
X. Initially 2 kg of A and 3 kg of B are put together in solution. One kg of X forms in one
minute.

Set up the appropriate differential equation expressing dx/dt
as a function of x.

... So like I'm stuck on finding dx/dt, please help!

Answer in back of book : 3k/16*(8-x)(4-x)   someone explain to me how to get to that please

[b^3]

ok so since the mass x is proportional
now we know the A 1:4 X
so as the reaction goes mass is lost from the inital 2kg of A so
same goes for b but B 3:4 X and initial is 3kgs
so
now sub that into the equation for dx/dt




then to solve it flip it and integrate it
Hope it helps

[kevinn_h]

omg ty that makes sense would never have gotten that myself thankyou thankyou

[b^3]

no problem, for the rest of the question, careful with the negatives when splitting it up into the partial fractions.