G. yedry - x = C, where C is an arbitrary constant. 14. Solve the initial-value problem for the exact ordinary differential equation. [5] 2xy - 9x2 + (2y + x2 + 1)y' = 0, y(0) = -3. A. y = =x'-1-yr +2r-+25 B. y= =x-1-v+123+2+2+25 C. y = =x'-1-v12r +2r-+25 D. y = =x2-1-v/2r-+25 E. y = =x2-1-v +12r +2r-+25 F. y = =x-1-vx*+2+2+25 G. y = =x'-1+2 412r- 42r-425 15. Solve the initial-value problem for the exact ordinary differential equation. [5] 2xy - 9x2 + (2y + x2 + 1)y' =0, y(0) = 2. A. y = =x'-1+vr +12r +2r-425 B. y = =x-1+vx4+2r2+25 C. y = =23-lty2r2+25 D. y = =x3-1-vx-12r +2x-+25 . E. y= =x-l+vx 412r +2r-+25 F. y = ='-1+v123+2+2+25 G. y = =x-1+vx-42+2+25 16. Solve the initial-value problem associated with the exact ODE. [5] (343 eazy - 1) + (2ye3zy + 3xyleazy) dy = 0 y(0) = 1 A. yedry - sin(x) = 1. B. y?e3ry + x2 = 1. C. yeary - In(x + 1) = 1. D. yeary + x = 1. E. ye3ry - r = 1. F. ye3xy - x2 = 1. G. yeary + In(x + 1) = 1. 17. Solve the initial-value problem associated with the exact ODE. [5] (341 - 21) + [In(12 + 1) - 21 =0 y(5) = 0 A. yln(1 + 12) - 12 + 2y3 + 25 = 0. B. yln(1 + (2) - 12 - 2y + 25 = 0. C. yln(1 + t2) - 12 - 4y6 + 25 = 0. D. y3 In(1 + t2) - 12 - 6y7 + 25 = 0. E. yln(1 + (?) - 12 - 2y3 + 25 = 0. F. y? In(1 + t?) - 12 - 2y' + 25 = 0. G. yln(1 + t2) - 12 - 2y? + 25 = 0. 18. Solve the initial-value problem [5] dy d y(1) = -1. A. y = -V2 - x2 B. y = -V2+x- C. y = -V2+ 12 D. y = -v2-x-I E. y= -2+x-2 F. y = -2-x2 G. y = -V2-1-2 19. Solve the initial-value problem [5] dy da = 2: y(2) = -1. A. y = In |x/2|-4 B. y = In x/2 - 18 C. y = In |x/2-6 D. y = In x/2 -2 E. y = In x/2-16 Ar F. y = In |x/2)-8 G. y = In |x/2)-2011. The general solution of the exact ODE (y cos(x) + 2xev) dax + (sin(x) + x2e" + 2) dy = 0 is [5] A. (sin(x) + xle" + 2)y = C. where C is an arbitrary constant. B. ysin(x) + x'e + 2y = C. where C is an arbitrary constant. C. (ycos(x) + 2xe") x + (sin(x) + axle" + 2) y = C. where C is an arbitrary constant. D. (ycos(x) + 2re")r = C, where C is an arbitrary constant. E. [(ycos(x) + 2re")dr + /(sin(x) + xle" + 2)dy = C, where C is arbitrary constant. F. -ycos(r) + xle + 2y = C. where C is an arbitrary constant G. y' cos(r)/2 + axle" + 2y = C, where C is an arbitrary constant. 12. The general solution of the exact ODE 2ty 12 + 1 - 2t ) dt + [In(t2 + 1) - 2] dy = 0 is [5] A. yln(t2 + 1) + (2 - 2y = K, where K is an arbitrary constant. B. y? In(t? + 1) - 12 - 2y = K, where K is an arbitrary constant. C. yln(t2 + 1) - 12 + 2y = K, where K is an arbitrary constant. D. y - In(t2 + 1) -12 - 2y = K, where K is an arbitrary constant. E. yln(t2 + 1) - 12 - 2y = K, where K is an arbitrary constant. F. y In(t2 + 1) - 12 - 2y? = K, where K is an arbitrary constant. G. y + In(t2 + 1) -12 - 2y = K, where K is an arbitrary constant. 13. Integrate the exact ODE [5] (3y eazy - 1) de + (2 ye3*v + 3xyl e3ry) dy = 0 A. yeazy - r* = C. where C is an arbitrary constant. B. yeary - r = C. where C is an arbitrary constant. C. yeazy - x? = C. where C is an arbitrary constant. D. yeazy - 3 = C, where C is an arbitrary constant. E. y? = eazy - r + C, where C is an arbitrary constant. F. yeary - r = C, where C is an arbitrary constant.\f