help on Differential equations HW

UTSA, Math 3613 003, Differential Equations I Fall Semester, 2014 Homework 3 Due November 18, 2014 Instructor: Dr. Ivanka Stamova Student Name: …………………………………………………

1. (3 points) Find 0

)( k

k k xaxy such that:

(a) yyx (b) 1xyy , 0)0(x , 1)0(x

2. (1 point) Show that if )(1 xy and )(2 xy are two linearly independent functions, and 0)(xz on I , then )()( 1 xyxz and )()( 2 xyxz are also linearly independent on I

3. (1 point) Show that if )(1 xy and )(2 xy are two linearly independent functions,

then so are their linear combinations )(3)(2 21 xyxy and )(3)(2 21 xyxy

Total: 5 points