"V If an initial condition is given, find the corresponding particular solution. Throughout, primes denote derivatives with respect to x. 1. y' + y = 2, y(0)=0 2. y' - 2y = 3et. y(0) = 0 3. y'+3y=2re-3 4. y'-2xy = et 5, xy' +2y=3x, y(1) = 5 6. xy' + 5y = 7x2, y(2) = 5 7. 2xy + y = 10 9. xy'-y = x, y(1) = 7 11 xy + y = 3xy, y(1) = 0 12. xy +3y = 2x, y(2) = 1 13. y' + y =e. y(0) = 1 14. xy -3y = x, y(1) = 10 15. y' + 2xy = x, y(0) = -2 16. y'= (1 - y) cos x, y(x) = 2 17. (1+x)y' + y = cos x, y(0)=1 18. xy' = 2y + x cos.x 19. y' + y cotx = cos.x 20. y'= 1+x+y+xy, y(0) = 0 21.xy' = 3y + x cos x, y(27) = 0 22. y' = 2xy + 3x exp(x), y(0) = 5 23. xy' + (2x-3)y= 4x 24. (x+4)y' + 3xy = x, y(0) = 1 8. 3xy' + y = 12x 10. 2xy' - 3y=9x dy 25. (x+1) + 3xy = 6x exp(-x), y(0) = 1 dx ilini