How would you solve these? (I use your explanations and answers as reference to my homework, because the summer teacher is out of reach oustide of class).

1) find an explicit general solution of the differential equation:

y' - 2xy= e^(x^(2))

2) Find an explicit general solution of the differential equation:

xy'= 2y + x^(3) cosx

3) Find an explicit general and particular solution of the initial value problem:

xy' - y= x, y(1)= 7

4) Find an explicit general and particular solution of the initial value problem:

y' + y= e^(x), y(0)= 1

5) A 400-gal tank initially contains 100 gal of brine (salt water) containing

50 lb of salt. Brine containing 1 lb of salt per gallon enters the tank at

the rate 5 gal/s, and the well-mixed brine in the tank flows out at the rate

of 3 gal/s. How much salt will the tank contain when it is full of brine?

(Solve questions using linear first order equation method primarily.

If you have any other methodic approaches to this problem, please

feel free to demonstrate).