Two-Point Boundary Value Problems - Numerical Methods in Engineering with MATLAB - page 310

11. Solve the boundary value problem

1
x y +

y + y (2) y = 0 y (0 . 01) = 1 = 0

and plot y vs. x . Warning : y changes very rapidlynear x = 0.

12. Solve the boundary value problem

y − 1 e − x y − = 0 y (0) = 1 y ( ∞ ) = 0

and plot y vs. x . Hint :Replace the infinitybyafinite value β .Check your choice of

β by repeating the solutionwith 1 . 5 β . If the results change, youmust increase β .

13. Solve the boundary value problem

1
x y +

1
x 2 y +

y =− 1( y ) 3 0 .

y (1)

y (1) = 0 = 0 y (2) = 1

14. Solve the boundary value problem

y + 4 y + 6 y = 10

y (0) y (3)

y (0) = = 0 y (3) − = 5

15. Solve the boundary value problem

y + 2 y + sin y = 0

y ( y (1)

y ( − 1) = 0 − 1) =− 1 = 1

16. Solve the differentialequationinProb. 15 with the boundary conditions

y ( − 1) = 0 y (0) = 0 y (1) = 1

(this is a three-point boundary value problem).
17. Solve the boundary value problem

y (4) xy 2 =−

y (0) y (1) y (1)

y (0) = 5 = 0 = 0 = 2

18. Solve the boundary value problem

y (4) 2 yy =−

y (0) y (4) y (0) = = 0 y (4) = 0 = 1