Apps. and Interpretation for IBDP Maths Ebook 2 | Page 325

www . seprodstore . com 315 20 ( c ) ( 1 ) Suggest a relationship between the distinct real eigenvalues of M and the coefficients of d d y x and y in 2 2 d d 4 12 0 d d y y y x x � � � . ( 2 ) Hence , write down the corresponding second-order differential equation for a general coupled system � Y NY , where N is a 2 2 � matrix , d d d d v x y x � � � � � � � � � � � � � Y , v y � � � � � � � Y , and the characteristic polynomial of N is given by 2 0 b c � � � � � with distinct real roots . [ 4 ] ( d ) Using the above results , for the second-order differential equation 2 2 d d 12 27 0 d d y y y x x � � � for which d 15 d y x � and 3 y � when 0 x � , find ( 1 ) the general solution ; ( 2 ) the particular solution . [ 8 ]

www . seprodstore . com 315 20 ( c ) ( 1 ) Suggest a relationship between the distinct real eigenvalues of M and the coefficients of d d y x and y in 2 2 d d 4 12 0 d d y y y x x � � � . ( 2 ) Hence , write down the corresponding second-order differential equation for a general coupled system � Y NY , where N is a 2 2 � matrix , d d d d v x y x � � � � � � � � � � � � � Y , v y � � � � � � � Y , and the characteristic polynomial of N is given by 2 0 b c � � � � � with distinct real roots . [ 4 ] ( d ) Using the above results , for the second-order differential equation 2 2 d d 12 27 0 d d y y y x x � � � for which d 15 d y x � and 3 y � when 0 x � , find ( 1 ) the general solution ; ( 2 ) the particular solution . [ 8 ]