In each of the problems
(a) draw a direction field for the given differential equation
(b) based on an inspection of the direction field, describe howsolutions behave for large t.
(c) find the general solution of the given differential equation, and use it to determine how solutions behave as t throughinfinity.
2. y'-2y=t2 e2t
3. y'+y=te to the -t+1
4. y'+(1/t)/y=3cos2t, t> 0
5. y'-2y=3e to the t
9. 2y'+y=3t
10. ty'-y=t squared to the -t, t> 0
12. 2y'+y=3t squared

Ernest is purchasing a $175,000 home with a 30-year mortgage. he will make a $15,000 down payment. use the table below to find his monthly pmi payment.

The table shows the relationship between the number of cups of cereal and the number of cups of raisins in a cereal bar recipe: number of cups of cereal number of cups of raisins 8 2 12 3 16 4 molly plotted an equivalent ratio as shown on the grid below: a graph is shown. the title of the graph is cereal bars. the horizontal axis label is cereal in cups. the x-axis values are 0, 20, 40, 60, 80,100. the vertical axis label is raisins in cups. the y-axis values are 0, 10, 20, 30, 40, 50. a point is plotted on the ordered pair 40,20. which of these explains why the point molly plotted is incorrect? (a) if the number of cups of cereal is 40, then the number of cups of raisins will be10. (b)if the number of cups of raisins is 40, then the number of cups of cereal will be10. (c) if the number of cups of cereal is 40, then the number of cups of raisins will be 80. (d) if the number of cups of raisins is 40, then the number of cups of cereal will be 80.

Me its important ! marge runs an ice cream parlor. her speciality is triple chocolate sundaes.she can prepare 1 sundae every 2 minutes, and she earns $1.20 for each sundae she makes . if she just makes sundaes for a single shift of at most 4 hours and at least 2 hours , which function relates her earnings to the number of minutes she works?