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(MATH150)2001_spring_final_exam.pdf
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Math150,FinalExam,Spring2001
1.SolvethefollowingEuler'sequation(8pts)
200
ty+5ty0+13y.0.t.0:
2.Findthesolutionofthefollowinginitialvalueproblem(8pts)
000
y+2y+5y..(t;2)+5u2(t).y(0).1.y0(0).;1:
3.Solvethefollowinginitialvalueproblem(Hint:youmayusetheconvolutioninte-
gral.8pts)
(4);t4000
y;81y.e.y(0).y00(0).y(0).0.y0(0).6:
4.Findthegeneralsolutionofthesystem(8pts)
..
3;4
0
~.x:
x~
1;1
5.Findthesolutionofthefollowinginitialvalueproblem(8pts)
.. ..
1;13
0
~x.~~:
x.x(0).
5;32
6.Findthegeneralsolutionofthesystem(10pts)
....
;2t
11e
0
~.x+:
x~4;2;2et
1