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3. Roughly sketch the solution of the following boundary value problems. Use the
sketch to estimate
y
(0) for each problem.
(a)
y
=−
e
−
y
y
(0)
=
1
y
(1)
=
0
.
5
(b)
y
=
4
y
2
y
(1)
y
(0)
=
10
=
0
(c)
y
=
=
=
cos(
xy
)
y
(0)
1
y
(1)
2
4.
Using a rough sketch of the solution estimate of
y
(0) for the following boundary
value problems.
(a)
y
=
y
2
y
(0)
+
xy
=
0
y
(1)
=
2
2
x
y
−
(b)
y
=−
y
2
y
(0)
=
0
y
(1)
=
2
(c)
y
=−
x
(
y
)
2
y
(0)
=
=
2
y
(1)
1
Obtain a rough estimate of
y
(0) for the boundary value problem
5.
y
+
5
y
y
2
=
0
y
(0)
y
(0)
=
0
=
1
y
(1)
=
0
6.
Obtain rough estimates of
y
(0) and
y
(0) for the boundary value problem
y
(4)
2
y
+
y
sin
y
+
=
0
y
(0)
y
(1)
y
(0)
=
=
0
y
(1)
=
5
=
0
7.
Obtain rough estimates of
x
(0) and
y
(0) for the boundary value problem
2
x
2
x
+
−
y
=
0
x
(0)
=
1
x
(1)
=
0
y
2
y
+
−
2
x
=
1
y
(0)
=
0
y
(1)
=
1
8.
Solve the boundary value problem
y
+
2
x
)
y
2
(
1
−
0
.
=
0
y
(0)
=
0
y
(
π/
2)
=
1
9.
Solve the boundary value problem
y
+
2
y
+
3
y
2
=
0
y
(0)
=
0
y
(2)
=−
1
10.
Solve the boundary value problem
y
+
sin
y
+
1
=
0
y
(0)
=
0
y
(
π
)
=
0
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