Question

find 2nd solution Y2 with order

II. Conteste las siguientes preguntas (30%) 21. (15%) Dado que y=2?cos (In 2) es solución de ??" - 3y + 5y = 0 halla una segunda solución y usando reducción de orden. Son yı y 2 linealmente independientes en el intervalo (1,2)? Justifique su respuesta

reduction

differential equations

Answer 1

The D.E oan to written as Where D = d m given (202-3207 5)y=0 z = logx then (n DE d² 21 22 put Whene D'= d az xD = 012 D) dz² Home the D.E becomes So ats mz 2 t i Hence (012_0'-30'+5)y=0 > (012 40'+5)y=0 m² 4m+5=0 auximary eque in -> (m-2)=-1 =) its general sol" is (where a,,C2 y = eae (e, Cosz + C2 Sinz) oring arbitrary -Ler coeloga) + cz sin (logo) constants) ez = x) sol" is Sin (109x) two Hence the of their 42 - 2 Sin