Question

Can someone help me with this problem?

Solve the following initial value problem de 23 (2)+3 (do (z)) – 10y (2) = -24 el–22) with y(0) = 2, dy(0) dc = -18

Answer 1

--- da2 with d2 yca) + 3 Cola y («)) -10 y) = 1-24 0-24 yco)=2, dyco) -18 da ted y=ema be a treicel solution, then aunitary equation of giren equation 0 rs m2 +3m-10 =0 m²+5m- 2am-10=0 mcm+5)-2 (m+5)=0 22 cm-2) cm+5) IO mr21.5. Henco complementary function is arbitrary constand Next we heme for Ypcan (-240-27) +30-10 [ where DE = ) Where AB are Gelas = Aeroa & Be 2x a particular indegrul 1 2 bo? d dz I d 2 e-2x d x2 - 24 D2+3D-10 (D++ (D+5)(0-20 e-2x 2-24 24e-27 (-2+5)(-2-2) 24e-24 3 c-a) 2 e-20 4 2 Hence general solution of ors You) = Call & Gold) = A e-57B e 2n+2e-2x Now given y com=2 ) 2 = A +B+2 => A+B20 - dd (2= d.o. of A e-se ny 5A e-5x42 B e2x_4e-2 Given dyo) da =-18 => -18 I -5A +2B-4 => 5A-2B=14 LO 27 50+ be? +20-21 da

IA = 14 Dang ♡ x2 + 2A + 2B=0 5A-2B = 14 + DA= 2 From ☺ B =-A = -2 Hence the required solution of or YCH) - 20-59_2222 +2e-2X