Question

Q2: choose the right answer: 1. Determine whether y = e3t is a solution of ý – 49 – 4y + 16 y = 0 ? ( a. y is not a solution b. y is a solution ) if you selected (a.), write only y = .... as the right solution. 2. Determine C, and C so that y(x) = Cje2x + Czet + 2 sin x will satisfy the conditions y(0) = 0 and y'(0) = 1? (a.{C=1,C=-1} b. {C=-1, C=1} c. {C=-1,C=2} d. {C=2, C;=-1} 3. Determine whether the equation y' 2xyey x2 + y2 sin is homogeneous? (a.it's not homogeneous b. it's homogeneous) 4. Solve axa-1 yb dx + bxºyb-1dy = 0 for nonzero values of the real constants a and b? (a. y = C2x + Cix b.y = C2xb/a C. y = 5+ Cixa/b d. y = czx-a/b) (10 Marks)

Answer 1

let y = e't .: 8- 2e24 8 - 9e24 8 - 21e38 - 27е - ч. зех - Ч. 3 + 16 е 34 7. 8. Чечня 16e1 y=eht is the right solution. 1. Given differential equation is 8- 4 - 4j t16 d=0 ... 8 – 4- 48 +16 8 not satisfy © option @ is true. satisfy the equation ③ (21 - 36 - 12 +16) еэ! = -5 e3k + 0 8.3 8 - ek let 64 e4k у - чј – 48+16 7 64e4k - Ч. 16 ed - 4.4, e+ 4 tigert ( 64 — 64 — 16 tts) е 14 8. е.

2. y (21) = C, p2x + ( 82 + 2 sink Y '(X) = 246 2x + Cl² + 21054 Y(o)=0 C, + (₂ +2.0=0 => Cit(=0 YO) = 1 26, + 12 + 2005 (0) = 1 261 + sincolo e al 1°) = -1 i cos(0) = 1 :. 24,+ (2.=-) (+4=0 C = -1 ہے۔ را b is true. .: option Given equation is alg Y'= 20 ye 3. hty?sin (2) 42 {2 (2) enzy + sin(a)} I'= 2(/) early (23)² + Sin (24)

8 - C, X-4/4 y's P(4) azez 7²+ sinz Wag or 41,585-44 where 8 (7) = Its a homogeneous equation. option is true. Given differential equation is аха-'96 4х + bx®ge" d = 0 xagbypas Ч) В. or ка 95 a х ть d9 we have integrating old x 4 blad - Isic, ų be the arbitrary J•3(«° 1%) - Јас у је - С. constant. г) 9 8 = cs 1-4 c, s. ke the arbitrary constant option @ is true,