Graphics Programs Reference
In-Depth Information
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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