Question

X(0) -90020 4) Solve for lup's - [-3x K te 42 12x7 at

Answer 1

dx dt 1-3 X dx 1-3% = dt integrate it we get In 21-3x1 = tt (ज) cult X (6) có at t=0, XCO so fea So eq. (1) becomes = 1/2 In 11-3x = t - 1-3x = -3t e -3t te3 x=24 (2) Scanned with CamScanner

it is given that dy - 2+ 2x -Y dy + Y 2 + 2x dt MT dy at + y = 2+ ? (1-etty (: eq@ 20 T dy at +y 2 -3t 63) [1dt = e (first orden tinear differential E9.) integrating factor et multiply e both side in eq. (3) we get let dy ety) get. Ze? dlety) & et zett et -2t 8 dt با 2t 3 dt side with respect integrate it both festos toh we get

et y Lt) & et 2 -2E e E2) tc 3 zt + + ē + c (4) u sy . 100 so & + te 3 W w 8 e so es (4) becomes et ya) . & et + + 6 24 - 3 & ytu ( at et set & & 1 e 3t zet So solution is H-e-34) &+ test zet SIM (4) (t) = & X (t) CS Seartrecht Can Scanner Yt 3