Question

in a certain chemical reaction, x grams, of a substance present is decreasing. the rate of decrease of x is proportional to the product of x and the time, t seconds, since the start of the reaction. Thus x and t satisfy the differential equation dx/dt = -kxt, where k is a positive constant. At the start of the reaction, when t=0,x=100.
i) Solve the differential equation, obtaining a relation between, x k and t.

Answer 1

i will get it started
$$
\Large{ dx/dt = -kxt\\

\frac{dx}{x}= -k t dt\\


\int {\frac{dx}{x}}= \int -k t dt


}
$$

Answer 2

Oops. Sorry was late.