Question

8. Determine the appropriate form of the particular solution for the following non-homogeneous linear differential equation with constant coefficients. * (8 Points) +9y" = 5 + e* (x – 3) + 4sin (3x). y (4) A + B sin(3x) + Cxsin (3x) + Det + Exer none of these A + Bxe-3x + Cxe3x + Det + Exet Ax2 + Bxe-3x + Cxe3x + Det + Exer Ax + B + C sin(3x) + Dcos (3x) + Exer Ax2 + Bx cos(3x) + Cxsin (3x) + Det + Exer

can you solve this problem please?

Answer 1

4144 gy':5+(2-3) + 4 sint 3x) (04+90239 = Ste" (2-3) +44in1 3*) ausilliury equation > m + g my oo mm +9) a m=0,0, +32,-31 0 so Cif.ay y = 6 +62) 208 + (z con B2)+Cufin(32) y = (GAGs) + Glos(2x) + Cafin (3x) p.1.) 15+ 0812-3) + 48in3x) (4+9D 9) [5+ e(2-3) +48inzx] 0²t0²tg) (5) + We ala-1 (4 sina) D21049) D²20249) D2D²tg) 20 + buots 5 > CS let) ./. (2-3) + Scagned with (OH) (DH)²+g + (4) (simsx) D%D79) CamScanner

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5 g teto ( 10 102-30-22 10 3] + 2 / 2. AUR (30) 2 acos Bal) ए g t el 104-52) + 27 hence pis piis 5 9 + en llox-32) + 3 n 20132 100 27 so solution & Ciftp.1 Y= G+Gxt C3 C8538 tlusinza +5 to t ea (lox-525+2 4 6x3x 10 22 Y A+B x te cosin + D sinax + (108-52) 7 0 ܐ + 2 x cosa 27 option (B) is correct. CS Scanned with CamScanner