from problem 22 to 28 we must arrive at the solution by the exact method

22. 2xy dx + (12 - x2) dy = 0. SOL. *2 + 12 = cy. 23. (xy2 + y - x) dx + x(xy + 1) dy =0. SOL. x2y2 + 2xy - x2 = c. 24. 3y(x2 - 1) dx + (x3 + 8y - 3x) dy = 0; cuando x = 0, y = 1. SOL. xy(x2 -3) = 4(1 - 12). 25. (1 - xy) -2 dx + [yz + x2(1 - xy)-2] dy = 0; cuando x = 2, y = 1. SOL. xy4 - y3 + 5xy - 3x = 5. 26. (3 + y + 2yz sen2 x) dx + (x + 2xy - y sen 2x) dy = 0. SOL. y2 sen 2x = c + 2x(3 + y + 12). 27. 2x[3x + y - y exp (-x2) ] dx + [x2 + 3y2 + exp (- x2) ] dy = 0. SOL. x2y + 13 + 2x3 + y exp ( -x2) = c. 28. (xy2 + x - 2y + 3) dx + xy dy = 2(x + y) dy; cuando x = 1, y = 1. SOL: (xy - 2) 2 + (x + 3)2 = 212 + 15