Question

(1 point) Given a second order inear homogeneous differential equation az(x) + we know that a fundamental set for this ODE consists of a pair nearly ndependent solutions . linearly independent solution We can find using the method et reduction of (2) + Golly=0 But there are times when only one functional and we would e nd a con First under the necessary assumption the a, (2) we rewrite the equation as * +++ (2) - Plz) - ) Then the method of reduction of order gives a second linearly independent solution as (0) Oyu-Cola) de ol Forecamp, where is an arbitrary constant we can choose the artitary constant to be anything we the One useful choice is to choose C so that all the constants in front 32- C35 then we can choose C - 1/3 so that 24 Given the problem ry" - Szy' + Dy0 and a solution i n Applying the reduction of order method to this problem we obtain the following ange p(z) = So we have EM vile) Finally, after making a selection of a value for C as described above you have to choose some nonzero numerical value wave at (7) C + 9 So the general solution to 9"-+ 4y = 0 can be written as y =

Answer 1

22 y "-skyltag ... given 91 =23 Prz) = (- / Spalda e sos de Sense) & laras) PC1) Әя as lo 9, Tar) "- cy, ur cx3 ensal. choosing CE! 92 (0) 2 173 en la!.

qy" - y'+ay =0 C2020+4) y -0. f(0) = 902-0+4 A.E is &M) = 0 am²-m + 4 =0

m. II 1-4(2)(4) & 1 I vits i 2.9. Yo eta [cacos (Vigs x) + q sin (193x)].