MATH 4B Lecture Notes - Lecture 8: Eigenfunction

• School: UCSB
• Department: Mathematics
• Course: MATH 4B
• Professor: Kelz J M

Document Summary

Solving inhomogenous problems via the annihilator method a better way to find all solutions to y ty. Cdkdcdhy-ef. tl/wsctscdidy-- o repeated roots solutions looks like y = a cost tczsihttcztcosttcyts. int take. Differential operator t annihilate a function gits it ( eigenfunction with eigenvalue o ) De "t e- to c dt dee o. I dtd annihilate e- t t e . g . "t 3y toy = e- y homogenous solution : et et. =o hers homogenous solution y =l , eat e- ttcztet then plug. ) c - et - e- ite "t. C 3 =/ solution : y =l , etta ett stet. I : a is an eigenvalue of gots under d. then. :x is repeated eigenvalue . ( d - xy l htt t. Cd - d7htset=o t gets = e: g. solve y" D5ldtdy = o has solution ! y=et4t"t cst. Cd - 2) cd-25g = cd - 2) eeo.