Find h(t) given h'(t): The concentration, h(t), of a chemical reactant in a 2nd order

[tsj1114]

The concentration, h(t), of a chemical reactant in a second order chemical reaction isis governed by the differential equation h'(t) = −k(h(t))^2, where k > 0 is called the ”rate constant.” Assume the concentrationat t = 0 is some given number h0. Determine h(t). Show all steps.

 

[HallsofIvy]

The concentration, h(t), of a chemical reactant in a second order chemical reaction isis governed by the differential equationh0(t) = −k(h(t))2, where k > 0 is called the ”rate constant.” Assume the concentrationat t = 0 is some given number h0. Determine h(t). Show all steps.

What you have written is very difficult to read. I assume you meant "h'(t)" rather than "h0(t)". Further, it is clearer to use "^" to indicate powers rather than just write the power after the formula. That is, I think you mean

h'(t)= -k h^2(t).

Of course, h'(t) is the same as dh/dt. We can write dh/dt= -k h^2 as dh/h^2= -kdt or h^(-2)dh= -k dt.

Integrate both sides.

No, I won't "show all steps". That is your job.