Question

In each of Problems 1 through 12: (a) Draw a direction field for the given differential equation. (b) Based on an inspection of the direction field, describe how solutions behave for large t. (c) Find the general solution of the given differential equation, and use it to determine how solutions behave as t → ∞.

Mainly need to be shown how to make the direction filed by hand

Answer 1

Please give me ?

Answers in Direction field 1aly +39 -t te cilin CS +7 117 Trillil!!!! b) for goes lastige t, the solution in disection field. to infinity - --- e) y'tay at the et e +34 = (t tet) I.F = ESPASA = P3 Yes - Setetet) et 4.3t = Site") at the do yen. De Semat - S6 (5) Sefun)]+(et)+c integration constant

yet. [+($)- Sevc34) dt} +(+c year THB +(e)+C. Y = 1/3 ha te 3 + cest y = 2/3 6 teht + cest 4 = 2 - 3 - 4 + ettc = (yoo , too) te w I!-- -- - - - arrocco b) from the direction field, for large values of t he solution cusues are approaching to y=1 too! It YCF) = 1

y'+y=tett Integrating factor is Sidt se genesal Solertion is yet =S (te* +) etat yet = S(tret) at Yet = // t tettc Y = 1 {tettetcet As t o the solution tends to L that is y (4 +14 (4) = 1 4= (& te&titc)