00:01
My students, let me explain to the question here.
00:02
We have to consider the following system of differential equations, of differential equations known as jacob monod model, jacob monod model, that is for population of species, population of species, x that feed on nutrients that feed on nutrients y so that is d x by d t is equal to v x y by k plus y into 0 is equal to 100 then d y by d t the d y by d t that is equal to minus v x y by s into k plus y y y into 0 is equal to 150.
01:19
So we have to use euler's method, euler's method for systems by hand with h is equal to 0 .1 to approximate the population of species at time is equal to 0 .3 and v is equal to 1 .4, k is equal to 250, s is equal to 10.
01:52
So coming to the solution here.
01:56
So the jocop monot from population jacob monot from population of species x, jacob monard from population of population of species x that feed on nutrients y, that feed on nutrients y.
02:33
By d t that is 1 .4 xy by 250 plus y x0 is equal to 100 so y -dash t that is dy by d t so that is minus 1 .4 xy by 10 into 250 plus y that is y now y into 0 that is equal to 150 so here we have to use ulers ulers iteration formula so what is the uller's atteration formula that is tn is equal to t0 plus nh that is n is equal to 1 2 3 so x n is equal to x n minus 1 plus h x dash t n minus 1 t n minus 1 so here x 2 is equal to 105 05 .25 1 .4 into 105 .25 into 149 .475 divided by 250 plus 149 .475.
03:58
So into 0 .1.
04:02
So whenever we calculate this, we'll get x2 is equal to 110 .7352.
04:08
Then y2 is equal to 149 .4752.
04:09
Then y2 is equal to 149 .47 .7 .7 .7 .7 .2 .2...