1. x sin y+x2y = c 2. 3x²xy² + c = 3. cx²+x+ y² = c h 4. y = mx + ; hi a parameter, m to be eliminated 5. y² = 4ax - m 6. y = ax² + bx + c 3x 7. y=4+ C₂e³x 8. y = c₁e ax cos bx + c₂eax sin bx; a and b are parameters 9. y = c₁x² + C₂e²x 10. y = ce* +C xe*

The solution of dy -y'sinx is: Select one: a. y-cosx+ C O b. COSX-C C. CO5X + C d. y%3Dsecx+C

If x*y" + xy +(x? -y3D x>0 V1=x 2sinx and y=y,v. Which of the following equations satisfied by v Select one: a. (x 2 sinx)v" + (2x2 cosx)v' =0 O b. (x sinx)y" + (2x cosx-xsinx+xsinx)v =0 cosx - x 2 sinx+x2 sinx)v =0 C. (x 2 sinx)v" + (2x 2 cosx)v =0 (x 2 sinx)v" + (2x 2 cosx)v=0

If x*y" + xy' + (x? -)y=D x >0 ,V1=x 2sinx and y = y,v. Which of the following equations satisfied by v Select one: a. (x 2 sinx)v" + (2x 2 cosx)v' = 0 b. (x 2sinx)v" +(2x 2 cosx)v=0 C. (x2sinx)v" + (2x cosx – xsinx + x2 sinx)v' = 0 cosx - x 2 sinx + x 2 sinx)v' = 0 d. (x 2 sinx)v" +(2x2 cosx)v' =0

35) y = -4 sin x 6- 21 TC 2n 3T -2+ -4 - 4.

Evaluate dx 9. 1 - 4x² x2 2, 2 tan 3 3. -1 3 sec¬1 2 + C 3 ɔ+(x- 5 sec 3 2 -1 + C 3 2 2. -1 - tan x+ C 3 3

Choose the correct letter and write your complete solution.

Differentiate y = VIn x 2 Inx +1 A. 2(In x)2 3. Inx-1 3 (In x)2 2 Inx-1 C. 2(In x)2 13 1. D. 3) 2(In x)2 B.

Evaluate (tanx * dy/dx) - y = a а. у%3 -а + С (csCX) O b. None of the choices О с. у%3-а + C(cosx) d. y = -a + C(sinx) е. у %3 -а + С(secx)

solve xsinydx+(x2+1)cosydy=0