MATH 4B Lecture 5: MATH 4B

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

Document Summary

Lecture 05 (in)homogenous second order linear differential equations solve y. Y = t let - y = t. Y = y it get it gets e- tdt t e then recall ky it get. I dtl ) cd - 3)y=cdtdcdy -3g ) - = eh wit ) y te-hhetetsttae. tt#=hkte4e4dt=ite3ttc. e-ttge3t homogeneous solution . complex eigenvalues y. 12 = cd - 2) x-d linearly independent solutions : y. So i is the rotational matrix which rotates a vector. Rotational matrices : ( iii joint) cost tant. :*"shot ) cost to 9) tsint. to ) ett = cos cts tis "m lt ) wshih put y = Etc - sint y it e ti cost (eitgs cast tis int ) . ice it eitf - sint ti cost ceitj i cost t sint ) o. Write cos at ) and shut as linear combinations of ett and e- it since eit = cost ti sint it and e- cost isnt ei =2wst cost.