Differential Equations please show all work 5. (30 points) Solve the IVP using the method of...

C53576)/6+2)(51)) Is=1 ; y(o)=1 zet y (0) = 3 Apply laplace lang form both sides to above differential equalion, {{41} +5 L{s'} + 64{4} - elfety + L{y"+5y' +64 ] = l{zety yrs) -sy(0)=Y160) seny[s] [5+55+61-5-18757 Ś+1) (s+27 (541) Criven that el y" + sy't by y[s] - Code y [s] Bu 2 (543) St3 +6 Y[5] 2 =264) Y(3] [64255+6] =***=5 $35 (5+1). Dijeta 2 (5+8) (5455+6) 5+1 S+8 Shol + (5+3)(s+2). (643)S+2)(674) 1 А + + 2 : 1. Pita (O) A: و نور ) Welfar 2 B - $=-2 (-2+3)(2+1) St3X43)(5+1) .. 1 2 ant) 2 25 с (041) (-1+3)61+2) 1 645) (542) (64) 2 2 + (5+3)(5+2)(5+1) (5+3) (5+2) (5+1)

5+8 e-ye+4e-262 B 6+8 (5+2)(643) t А. S+ 2 S+ 8 A- 873) (6+3.) 7.(-2+8) 6. (SpA X6+3) ]/6--2 (243) (546) (5+8) (5+2) (543) -3+8 (5) -3+2 تزیا 5 B - 5=-3 CHE A $ (5+3) (52) (5+2)(5+3) 5 26 c5+2 - St3 1. t S+1 S+2 Y[5] => S+3 -4 4 + + Y(s] [cy 4 ($13) (5+2) (5+1) (Stay تن از on throw tol cyls] Apply Inverse laplace leansform sats - 9 Sim S+1 x + SARA St3 i'{4155} (d ten) . *}

[ey'Gt) 3 cest geet et in. 3. kail [email protected]): 1, 369-3 → s"+ y + y = 26, (0750+6)y=ect م (1) بيري 0 لیے (0) For chomogeneous We know that you bol (Deut su - (AJU G0²+5076- Tb (11756-1) +6 9-5 overall solution is cg= Th 4 Up = cott Geet et ot Then | Yh (G 2) he e Yp telu tre Diw (0+5046 29 Auxiliary equation D'450+6=0 (0+3) (0+2) -0. -0-43,-2 -et c est te . در فرد لرزه (*) For failiöilat (Solulión فرسا zet (02516) Yp st at e (0450+6) us f(0) eat ; falto fra) zet et (Bull solt et C G YpCt) 7 *C2710 9 y(0) y01 -8G+262-13 flom 6.-€ CAC2= -34 -26 = 4- -36, -2C2-4 3 362-262-4. 22=4 6--C--4. y(t) = -4e3t+meztetét