Do b, d, and g Also make sure to describe and identify the equilibrium solutions Exercise 2.3.2 Use whatever technology you have available to sketch a direction field for thegiven ODE on the specified range. If the ODE is autonomous, visually identify the equilibriumsolutions, if any.(a) u'(t) = u(t)-21 for 0 ≤t≤2 and 0 ≤u≤ 2.(b) u' (t)=u²(1)+1+1 for -2 ≤t≤ 2 and -2 ≤ u ≤ 2.(c) u'(t)=-u(t) for -2≤t≤2 and -2 ≤ u≤ 2.(d) u'(t)=-1/u(t) for-2≤t≤2 and -2 ≤ u≤ 2.(e) u'(t) = u(t) (u(t)-3) for -2≤t≤5 and -2 ≤u≤ 5.(f) u'(t) = (u(t)-1) (u(t) +1) for -2 ≤ t ≤5 and -2≤u≤5.(g) u'(t)=tsin(u)-12/4, -2≤t≤5 and -2 ≤u≤ 5.(h) u' (t) = cos(u+t) for-2≤1 ≤ 5 and -2 ≤ u≤ 5.Exercise 2.3.3 For each ODE sketch a phase portrait by hand, following the procedure ofExamples 2.10. 2.11. and 2.12. Classify each fixed point as asymptotically stable or unstable.ob,d and ghow transcribed dataONOV15átvÇalıZA

Direction field: A graphical representation of all the solutions of a first order differential equation is called a direction field. We have to sketch the direction field of the given first order differential equation within the specified range of u and t.Part b A differential equation of the form dudt=fu, t is called an autonomous differential equation when the function fu, t is a function of u only. The direction field of the differential equation u't=u2+t+1 for -2≤t≤2 and -2≤u≤2 is: The given differential equation is not autonomous because the function fu, t=u2+t+1 depends on both u and t.Part d The direction field of the differential equation u't=-1u for -2≤t≤2 and -2≤u≤2 is shown below: The given differential equation is autonomous because the function fu, t=-1u depends on u only. The equilibrium solutions are sketched as green curve in the below graph:Part g The direction field of the differential equation u't=tsinu-t24 for -2≤t≤5 and -2≤u≤5 is: The given differential equation is not autonomous because the function fu, t=tsinu-t24 depends on both u and t.