**Unformatted text preview: **C . C. Let A ∈ M n ( R ) be diagonalizable with P –1 AP = D = diag( d 1 , . . . , d n ) Show that Y ( x ) ∈ C' ( I ) n solves the system Y' = AY + B ( x ) with B ( x ) ∈ C ( I ) n ⇔ Z ( x ) = P –1 Y ( x ) solves the system Z '( x ) = D Z( x ) + P –1 ω B ( x ). Note that this latter system is a diagonal system that reduces finding Y to solving n first order LDEs. Use this approach to find a specific solution of the system: y 1 ' = –2 y 2 + 1/(1 + e –x ) y 2 ' = y 1 + 3 y 2 + 1/(1 + e – 2 x ) Hand In 12A) pp. 540-541 #6; 20; p. 545 #3; 8; p. 560-561 #12; 18 12B) p. 545 #4; p. 571–572 #8; 15; A Due Friday December 2 ....

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