Question

. Consider the IVP: y + 3y = e 3t, y(0) = 1, y(0) = 0 - Solve the IVP using the guess and test method. .Solve the IVP using the general formula for integrating factors. - Solve the IVP using Laplace Transforms. . Verify that your solution satisfies the differential equation (you should get the same solution using Il three methods, so you only need to test it once).

Answer 1

Joy y'+3y=ēto :400)= 1 iy.co=0 Cleanly O is Linear Diffentidegnalien Is of Hue form y'+ Pc+) y-Qc). whiere plt) = 3: Qct)-e er If Spetsdt echt= 3 lle geimal Solution is YCI-F) = S QUI fldt to yest-set yedt-se de yest ette 2 y = - 07-344 cest y=- ut & cest y'=. 4eut acest 900)=1 → 15-1+C = (52) Then y=-eut 2 e 3t / 1 Is segnized solution ( Scanned with CamScanner

now using laplace L{y'+34y = efekty L{y'y+31&y} = Styl sū- y0)+ 19 = sty g (5+3)+1 = Śty ġ = $t3 * 1664 $12964) - Pirates on sto say 5 S by using Poractions + non sont to stay ý = 2 443 sty applying inverse laplace Leģy=221&3}-{{sty} - Yt) = 2 e36 e46 ✓ CSScanned with CamScanner

Verification 0836 ent r we got y(t) = 2e3Fe y = -6e344eut + y = -xe ve" (a + 2++) - at yeuta Get Bett y't3y = è ut » D.E satisfied now 4 900) = 2e&=2-1=1 9'10) = -bety@=-6+4=-4 here initial conclition sio=0 is voilating - 0 CScanned with CamScanner