Question

Find a general solution to the given differential equation. 32y" - 12y' - 9y = 0 A general solution is y(t) = 0

Answer 1

Given that

soli given that differential equation 32y"-12y'-ay=0 then, let us change this equation to standard form by dividing Dein, by 32. 324" - 129'-ay=0 32 then, 32" - szy 3 ay 32 9"-3 3 y 1 - 2 / 220 2 By the charactenstic equation of @ is me 3 9 32 ZO. -bt th br_uac a=1, b = 3 9 ) 2a 32 ( 318 ) + ( uxix 32 2x 1 3/8 t 9 36 GU 32 2 X 2 9+ 3662 64 3 16 1 9-72 by

2 . 3 16 1 2 3 16 + 1 9. 2 3 1 9 8 2. + 3 16 9 16 3 -9 3 +9 16 ) 16 .. the Roots of the charactenstic equations 3 3 are m 3 16 4 & m2 16 8 Then, we & m₂ get distinct real roots Hence the general solution to the giren differential equation is Y(f) ac, emit + se 3/4t mat. -3/6 yet) acie te Ans.