Question

dy Find the solution of dt - 5y (4 – y), y(0) = 20. (Express numbers in exact form. Use symbolic notation and fractions where needed.) y =

Answer 1

dy dt 5 Y (4-y) Y(0) = 20 dy = 5dt => 74- => 14 ( 1 / + ) dy = 5d7 4-y I:0. Bis get we set => 3-4 ) dy linc + ln (A B = - ) dy = 5fdt 7-4 sh 20 Sdt 7 lny - ln (8-4) sot we have ena lno -> lm (1/4) = gott line ln y got y - 4 = lnl c(y-4) y (3-4) pot =7 y c(y-4) e zot zot 7 y-cze -4ce -7 y(i-ceact) = -4ce2t =7 -4ce y got ; ) २०४ に e =7 aot at got (t) y 1 - ce zot 4 ce 20t ce -1 -> (1) =7

put t=0, we get ૧ (૯) 4C C-1 Given yo) = Q 0 40 =7 20 C-1 20 - = 4 c => 200 => 16 C-po co 4 - 5 = 0 C -7 c =7 + ܩܐ 4 get e 3 (t) e 4 sub. ' ŕ value 'ľ value in (1), we zot 5 4. = 4 zot 5 -1 zot 5 e 207 5 e - 4 zot 2o e => Y cot 5e - 4 = =