Wolfram Mathematica coding

Help to write some Wolfram Mathematica for those statement: [login to view URL] distribution Suppose that demographic studies show that each year about 6% of a city's population moves to the suburbs (and 94% stays in the city), while 4% of the suburban population moves to the city (and 96% remains in the suburbs). In the year 2000, 59% of the population of the region lived in the city and 41% lived in the suburbs. Derive a function to give the population distribution for any year in the period 2000-2050. For simplicity, ignore other influences on the population such as births, deaths, and migration into and out of the city/suburban region. Use two methods: 1. Markov matrix multiplications 2. linear combination of eigenvectors For each method, construct a list of population distributions for the years 2000-2050. (Obviously, the two lists should contain identical values - but may be structurally different.) Plot the list. From the eigenvector approach, determine the stable population distribution (n->\[Infinity]). 2. 2.1 Compute the general solution to : dy/dx+(1/x)y=sin x 2.2 Solve the initial value problem: dy/dx+(1/x)y = sin(