Question

You have answered 0 out of 2 parts correctly. Consider the intial value problem: 644" + 80y + 25y = 0, y(0) = a < 0, y(0) = 5. a. Find the solution in terms of a. Give your answer as y=... . Use x as the independent variable. Answer: _ 5x 8 8 y=cle +62xe b. Find the critical value of a that separate solutions that become positive from those that are always negative. critical value of a =

Answer 1

envation in 64' + 80% +257=o. hat, y=ena be the trial salution of Ausiliaoy envation in 64 m² +8om +25=0 m= -80 + 2/(80) ²- 4.64-25 2.64 80to 128 - - 5 saletion is -52 7 (x) = ci é 8 + Caxé Where, cu ca 5e2 -52 are asbitrary constans by Differentiating @w.o.za d'a) = -5ee3 tee - 5 Griven conaition is 70) = a => a = cite2 => et ea ara, yo = 5 561 te2. * 5 = 8 27 sei- 8e2 = 40 -- Solving ② & ③ we get

3.0. = 13 (89.140) -C2 = a- 8 la+5) 13 13a - sa - 40 13 50- 40 13 3 3 (a-8) negative for agaço alaways a= 5, then e When - 5<a to the e, alaways positive. epitical value of a=-5 ya) = t3 (89+4 (sa+40 jet s (2-3) 5x -8ze 100