Would you be able to solve this problem? I have some answers but I am not sure if they are correct and would love some help. Thanks!

Demand relationships Consider a consumer maximizing the quasi-linear utility function u(x, y) = In(x) +y subject to the budget constraint pxx + pyy - M where all parameters are strictly positive. (a) Show that the (Marshallian) demand for good x is independent of income, whereas the (Marshallian) demand for good y is normal. (b ) Derive the own-, cross-, and income-elasticities of (Marshallian) demand for each of the goods. (c) Evaluate whether the consumer's preferences satisfy "homogeneity." (d) Evaluate whether the demand for each good satisfies "Engel aggregation." (e) Evaluate whether the demand for each good satisfies "Cournot aggregation."