Find the general solution of the given differential equations. give the largest interval i over which the general solution is defined. determine whether there are any transient terms in the general solution.

y' + 2xy = (x^3)

ydx = (y(e^y) - 2x)dy

(dp)/(dt) + 2tp = p + 4t - 2

Adj has a total of 1075 dance and rock songs on her system. the dance selection is 4 times the size of the rock selection. write a system of equations to represent the situation.

Aright cylinder has a diameter of 8 m and a height of 6m. what is the volume of the cylinder

Use the information given below, to compare the cost of operating two different vehicles for one month (4 weeks) you are considering two different cars. you drive to work, a 20 mile round trip, five days a week. gasoline costs you $1.50 per gallon car agets 28 miles per gallon, would have $300 a year in maintenance costs, and would cost you $1,500 per year to insure car b gets 19 miles per gallon, would have $500 a year in maintenance costs, and would cost you $1,000 per year to insure costs car a car b gas cost per month insurance cost per month maintenance cost per month $ total cost per month