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Midterm

MAT244H1 Midterm: Practice Test 1 Summer 2013 SolutionExam


Department
Mathematics
Course Code
MAT244H1
Professor
All
Study Guide
Midterm

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Mat 244 Practice Test 1 and Solutions
Jordan Bell
June 4, 2013
1. Solve the initial value problem
3y0+1
ty= 2, y(1) = 2.
Solution Rewrite as
y0+1
3ty=2
3.
Multiply by µ
y0µ+1
3tyµ =2
3µ.
We want the left hand side to be equal to (yµ)0=y0µ+yµ0. So we want
1
3tyµ =yµ0,
hence µ0
µ=1
3t.
Integrating,
ln µ=1
3ln t= ln(t1/3).
Hence
µ=t1/3.
Thus
(yt1/3)0=2
3t1/3.
Integrating,
yt1/3=1
2t4/3+C.
As y(1) = 2, we have
2 = 1
2+C,
so C=3
2, and hence the solution is
y=t
2+3
2t1/3.
1
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