In each of Problems I through 13, either solve the given boundary

value problem or else show that it has no solution. (Problems 11

through 13 involve Euler equations; see Section 5.4.)

1. y"+y=0, y(0) = 0, y'() = 1

2. y" +2y = 0, y'(0) = 1, y'(x) = 0

3. y"+y=0, y(0) = 0, y(L) = 0

y"+y=0, y'(0) = 1, y(L) = 0

4.

5.

y"+y=x, y(0) = 0, y(x) = 0

6.

y" +2y=x, y(0) = 0,

7.

y" + 4y = cos x,

8. y" +4y= sinx,

9. y + 4y = cos x,

y(0) = 0,

y(0) = 0,

y'(0) = 0,

y(π) = 0

y(x) = 0

y(x) = 0

y'(x) = 0