## Question

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

Differential Equations

please show all work

5. (30 points) Solve the IVP using the method of Laplace transforms AND one other method of your choice. y" +5y'+6y = 24' ; y(0)=1, y'(0)= 3 TABLE 72 Properties of Laplace Transforms {"}() = s£{f}(s) - (0) ${f"}(s) = 5248{f}(s) - 55(0) - f'(0) TABLE 21 Brief Table of Laplace Transforma F(s) - ${}}) 1 >O HI ! r. = 1,2,... 50 sin be >O cos br 50

## Answers

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

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