Math 4B Midterm Exam

10 points find the general solution of the

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(10 points) Find the general solution of the differential equation ty' + 2y = 3tet3, t > 0. *)<*) n M L V * V ' -f c ) l *5 V* 7 2 2 / ,'f -- y * © T Jf\ |4 V / 5. (10 points) Consider the initial value problem: y' = t2 + y2, 3/(1) = 0. Use Euler’s method with h = 0.5 to approximate 3/(2). -ÿ<? ~ V HP.. Y~ - i.* '1 {-t ,y- I- + C 71 0?'ÿ W9 V

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6. (10 points) Consider the differential equation y' = 32/ + y2 (a) Find any equilibrium solutions of the DE. ' -- v (!-"/) (Vi) V V O ' V M (b) Draw the slope field for the DE, and sketch the equilibrium solutions and three other solu¬ tions. \ 1 \y o N / 4L - 7 . /\ / /; Cb'ffi ~-'L j - 7r / / t r - V K 0 J -J T\ 1 - s (c) Classify any equilibrium solutions from part (a) as unstable, stable, or semistable. - 0 urd+y* -v& ) r-
/z i V e J A/f) AALP* - 'M* + y e l*\f V C e ytf -- A V1 3 e f’ / 0 X <w KMMW e* te w*ÿ* **»> Hr* ("»*ÿ'- J wt j<» Jo Ht ,A<t,«.(, HIM by £ bi’s-okit sM*. yÿ, So .V t> ,-> ft. for*** &f~

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