Question

9. 1/3 points Previous Answers ZillDiffEQ ModAp 11 2.3.024.3/6 Submissions Used My Notes Ask Your Teach Find the general solution of the given differential equation. (x? - 9) + 6y = (x + 3)? Y(X) - Give the largest interval over which the general solution is defined. (Think about the implications of any singular points. Enter your answer using interval notation.) Determine whether there are any transient terms in the general solution. (Enter the transient terms as a comma-separated list; if there are none, enter NONE.)

Answer 1

Given differntial equcetion is (229) dy + 6) = (x+3) 2 use. § x² - y2 = (x+y)(x-4) 22-9 = (x+3)(1-3) dy dx 22 2+3 2-3 compairing with dy + pex)) = g(x) =) pcx dx 2) 2 +3 x-3 Integrating factor is I. FELICX) = Spex) d2 6 - all(x) = - eleg dx S 70-9)dr we knoce x we know star a log ( 22 ) -a 2a2 29 ata

from @ ollar): + 3 2 3) *+3 (+9=3) 4 (1) - 1 ( 2 ) * *) . genral solutron is -x+3) YXu(x) = g(x) x 4(x) dx +6 - YX (26 1 ) = S(xt) (x-3) dx tc. =) YX (2-3) = ax + c a) y X (2-3) = xtc =) Yox) = x (x+3) + c(2+3) => [YCY) = (2x +33 ) + < ( *13) = x ) x+3 2-3 2t3 2-3 x-3 which Ý required sowion of given diff. equation y cX) is define when x #3 largenst interveel over y CX) define is (-c0,3) 0 (3 co) or (-0,00) / (3}

The such transient that upon o the term of ODE is a toom. taking the elmit as term tends to o in teg genral solution. eim x → 2-3 and eim el x+37 ein crit 36x 7 xool x-3) - x0 Li-31x -) с But cis any arbitory constant ! Chence e may not be zero) limit ther is no term as x y os term sulh that tends to the zerro. in the ... There is no genral solution of transient term given ODE.