Question

1. Consider the differential equation" = y2 - 4y - 5. a) Find any equilibrium solution(s). b) Create an appropriate table of values and then sketch (using the grid provided) a direction field for this differential equation on OSIS 3. Be sure to label values on your axes. c) Using the direction field, describe in detail the behavior of y ast approaches infinity. 2. Short answer: State whether or not the differential equation is linear. If it is linear, state whether on not it is homogeneous. a) S -30 + 11 = In (t - 7) y dt ty dt* b) ay-r="y+52 y 3. Using a theorem in chapter 2 and without solving the problem, determine the largest interval on which the solution of the given initial value problem is certain to exist. Show work. a) vt + 5 cos(t) - 2y = with y(- 4) = 0.5 b) vt + 5 cos(t) ay- y = with y(-0.5) = 1.25 4. Use a two-step Euler's Method to approximate y(1.2) if y = -2t + y with y(1)=3. 5. Solve explicitly the initial value problem wity with y(0) =- 2. 6. Consider the differential equation: x + y = g(t)with g(t) = {? (2t if 1st <2 16 if tz2 Find a continuous solution to this differential equation if y(5) =10.

Answer 1

By rules and regulations we are allow to do only one question at a time.. i solved two questions..

Doubt in any step then comment below.. i will help you..

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please thumbs up for this solution..thanks..

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a dy sy + la face-1) near homogeneous Not Uneaa dt ut yay= c enclat) + y = 2 (C=23 0+C 2= ylolar y = 4(lt enlift)) y = -2 Jit en Cift)