W AutoSave On MATH156_M10L1_PORTFOLIO . Last Modified: 17 March Search (Alt+Q) Danise Nicole David DN X File Home Insert Draw Design Layout References Mailings Review View Help Grammarly Comments Share Calibri (Body) v 11 IA BI U ab X2 X AD Normal No Spacing Heading 1 Paste Editing Dictate Editor Open ADVAv Aav A A Grammarly Undo Clipboard Font Paragraph Styles Voice Editor Grammarly 1 . . ..1 1 .1 . 1 .2 . 1 . 3 . 1 .4 . 1 .5 . 1 6 . 1 .7 . 1 . 8 . 1 .9 . 1 .10 1 11 1 12. 1 .13. 1 14 1 15. 1 16 2 1 . 1 . 1. 1. IF 1.) 3.) Write down a differential equation of the form - dy = ay + b whose Draw a direction field for the differential equation y' = -y(7 -y). Based on the direction field, determine the behavior of y as t - co. solutions all approach y = 17 gas t -+ co. If this behavior depends on the initial value of y at t = 0, describe this dependency. y' = 5 19 - 1 ) The two equilibrium solutions are y (t ) = 7 and y(t) = 0 .17. 1 .16 1 .15. 1 .14 1 .13. 1 .12. 1 11. 1 .10. 1 . 9 . 1 . 8 . 1. 7 . 1 .6 . 1 . 5 . 1 .4. 1 . 3 . 1.2 . 1 . 1. 1. 2.) Solutions with initial values greater than 7 Write down a differential equation of the form dy = ay + b whose diverge from the solution y(t) = 7. all other solutions diverge from y = 5 as t - co. Solutions with initial values between 0 and 7 decrease toward the solution y(t) = 0. y' =y-5 Solutions with initial values less than 0 increase toward the solution y(t) = 0. Page 2 of 13 20 words [ English (Philippines) Ex Accessibility: Investigate " Focus + 66% 33 . C ofi 0 ENG 4:13 pm P X o A CO Sunny US 04/05/2022W AutoSave On MATH156_M10L1_PORTFOLIO . Last Modified: 17 March Search (Alt+Q) Danise Nicole David DN X File Home Insert Draw Design Layout References Mailings Review View Help Grammarly Comments Share Calibri (Body) v 11 IA BI U ab X2 X AD Normal No Spacing Heading 1 Paste Editing Dictate Editor Open AD Av Aa A A Grammarly Undo Clipboard Font Paragraph Styles Voice Editor Grammarly 1 1.1..1 1 .1 . 1 .2 . 1 . 3 . 1 .4 . 1 .5 . 1 .6 . 1 .7 . 1 . 8 . 1 .9 . 1 10 1 11 1 12. 1 13. 1 14. 1 .15. 1 16 2 1. 1 . 1. 1. 4.) Where a = 8. Equilibrium solutions: aw a direction field for the given differential equation. Based on the direction field, determine the behavior of y ast - so. If this y(t) = 0 and y(1) = 8. avior depends on the initial value of y at / = 0. describe this dependency. Behavior of y(1) as 1 - co depends on initial value y(to): y = y(y - 8)2 y(to) > 0:y(1) - 8. y(to) 8: y(1) diverges fromy = 8. 0 (to) 8: y(1) diverges fromy = 8 0 0 dx 4x + 3xy2 NOTE: Do not enter an arbitrary constant. y = 12 t 7 197 6 5 7 4 60 t4 The solution in implicit form is 4xy tay -23 = C where C is an arbitrary constant. Page 9 of 13 20 words [ English (Philippines) x Accessibility: Investigate TO Focus + 66% 33 .C OLDO X 0 ENG 4:15 pm W P A CO Sunny US 04/05/202215.) Find the solution of the given initial value problem. 10 cost y = +-10 y( 7) = 0, 1>0 y(t) = 10 sin(t)15.] Find the solution of the given initial value problem in explicit form. 1 y\" = (1 3w}y2,y(0} = -3 17.] Find the solution of the given initial value problem in explicit form. 11' :r SW23) d3: + 006(61):) (3; = 0, 3(5) = E y(a:) = (1n: sin1(6 cosz(m))) J 1 6 1s.) Determine (without solving the problem} an interval in which the solution of the given initial value problem is certain to exist. (16 y' + Qty = 7:2, y(7) = 1 0 + er 3r + cr4 + ert 51 ST + er 1 31 + crd The following problem involves an equation of the form (ii: = f (3;) Sketch the graph of f (3;) versus 3;, determine the critical (equilibrium) points1 and classify each one as asymptotically stable or unstable. Draw the phase line, and sketch several graphs of solutions in the typlane. d df=y