Question 4 (2 points) Find the solution to the initial value problem (1 +e') +ely= Int, y(0) = 1. Question 1 (2 points) 723 - 723 + 2123 + o Find the general solution to the equation y(t) _ Int + 2 dt - ysint = 1 O O y(t) _ tit - t+ 2 v(t) = (t + C) eset 1 + et O O y(t) = (-t+ C) sect y(t) - Int -t+2 e za can be O 1+ et y(t) = (-t+ C) cset O 3(t) - tint + 2 y(t) = (t+ C) sect 1+ et where 13, 21, and 24 ca any real numbers No solutions. Question 2 (2 points) Question 5 (2 points) Find the solution to the initial value problem A 1,000-gallon tank is filled with 500 gal of pure water. A 2 - 23 4 323 + 284 - spigot is opened and a salt solution containing 1 lb of salt de - "Ite 2, y(0) - 0. per gallon of solution begins flowing into the tank at a 1 - 12+ 723 + 624 - 25 rate of 2 gal/min. Simultaneously, a drain is opened at 3r + 23 + 5x, + 624 - 35 O the bottom of the tank allowing the solution to leave the v(t ) - e' (- tan ' (e') ) tank at the rate of 1 gal/min. How many pounds of salt will there be in the tank at the precise moment that the volume of solution in the tank reaches the tank's u(t ) = e' ( #- tan ' (e-' ) ) capacity of 1,000 gal? (Please put only numbers up to two decimal points in the where za, Is, and za can be any blank). O u(t ) = e ' (# - tan ' (e-') ) O No solutions. o "(t) = e-' (# - tan ' (e')) Question 3 (2 points) where r , and zs can be any O Question 6 (2 points) Professor Farlow's Coffee Professor Farlow always has a cup of coffee before his where I s can be any real numbers . 8:00 am differential equation class. Suppose the coffee is 198 F when poured from the coffee po s to 134'F in a room whose wever , Professor Farlow nev drinks his coffee until it cools to 86 F. When will the Problem 18 in Section 2.2 Professor be able to drink his coffee? (Please put only numbers up to two decimal points in the blank ) Find the general solution to the differential equation 1 + 23+ 23 + 224 = 15 -21 - 23 + 723 + 624 - 2 ay _ _y=3+3. 32 1 + -323 - 224 - 35 O y ( t ) =t' + c 21 - 23 + 723 + 624 - 25 is. +5. +53. + 6FA - 35 o No solutions O O y ( t ) = t' + Ct2 O y ( t ) = t* + Ct where za can be y (t ) =t* + C+ 3 No solutions where 23. 23, and zs can be a MacBook Air where z , and z. can be any real me