Show all work for full credit! 4 problems- 25 points each with an initial velocity of 5 meters/sec and moves with acceleration a() aot. lt0.75 where ao is a constant for 45 seconds and then lifts off the end of the runway. how fast was the plane traveling (in meters/sec) on lift off? model and solve using differential equations. show all differential equations and all work. find the general solution (implicit if necessary, explicit if convenient) for the following: 2 (2 +x) 2 dx = (2 + y)2 3 verify that the differential equation is exact, then solve it. (6x-y)dx = (x-4y)dy 4 use the integrating factor explained on page 47 to solve the following: cy-ay = b + be-2ax where a b, a, b, c are constants. solve the differential equation.