Kindly write in a neat and organize way.

Instruction: using the topic of Homogeneous in differential equation choose at least 6 questions on the attached picture. Answer were already given. I need the DETAILED AND FULL SOLUTION (include the formula or theory used). Additional notes are NOT REQUIRED BUT GREATLY APPRECIATED. I'll give honest feedback; thumbs up if I'm satisfied, thumbs down if I don't see an effort. THE ANSWERS SHOULD BE SIMILAR TO THE GIVEN ANSWER ON THE ATTACHED. Thanks in advance.

Exercises In exercises I through 21, obtain a family of solutions. 1. (x - 2y) dx + (2x + y)dy = 0. ANS. In (x2 + y') + 4 arc tan (y/x) = c. 2. 2(2x2 + y?) dx - xy dy = 0. ANS. x* = c'(4x) + y). 3. xydx - (x] + 3y]) dy = 0. ANS. x2 = 6y2 In ly/cl. 4. xay' = 4x3 + 7xy + 2y'. ANS. x (y + 2x) = cly + x). 5. 3xy dx + (x] + ) )dy = 0. 6. (x - y)(4x + y)dx + x(5x - y)dy = 0. ANS. x(y + x) = dy - 2x). 7. (50 - u) du + (30 - Tu) du = 0. ANS. (30 + u) = co - u). 8. (x' + 2xy - 4y?) dx - (x] - 8xy - 4y?) dy = 0. ANS. x2 + 4y? = (x + y) 9. (x' + y?) dx - xydy = 0. ANS, . y = 2x3 In |x/c.10. x(x3 + y)(y dx - xdy) + y dy = 0. ANS. (x2 + y3)) = 6y In Ic/yl. 11. (x3 + y' ) dx + xydy = 0. ANS. x3(x + 2y]) = C'. 12. xydx - (x + 2y)' dy = 0. ANS. V (x + y) = ce. 13. o' dx + x(x + v) du = 0. ANS. xu = (x + 20). 14. [xcsc (y/x) - y]dx + xdy = 0. ANS. In |x/c) = cos (y/x). 15. x dx + sin' (y/x)[ydx - xdy] = 0. ANS. 4x In (x/c] - 2y + x sin (2y/x) = 0. 16. (x - ylny + yln x) dx + x(Iny - In x)dy = 0. ANS. (x - y) In x + ylny = cx + y. 17. [x - yarc tan (y/x)] dx + x arctan (y/x) dy = 0. ANS. 2y arctan (y/x) = x In [c'(x2 + y?)/x*]. 18. y' dy = x(xdy - ydx) eth. ANS. y In ly/c) = (y - x)eth. 19. 1(s' + 13) ds - s(s' - 13) dt = 0. ANS. $2= -212 In jest]. 20. ydx = (x + y' - x) dy. ANS. arc sin (x/y) = In ly/c). 21. (3x] - 2xy + 3y?) dx = 4xydy. ANS. (y - x)() + 3x)' = ex'. 22. Prove that, with the aid of the substitution y = vx, you can solve any equation of the form y'/(x) dx + H(x, y)(ydx - xdy) = 0, where H(x. y) is homogeneous in x and y. In exercises 23 through 35, find the particular solution indicated. 23. (x - y)dx + (3x + y)dy = 0; when x = 2, y = -1. ANS. 2(x + 2y) + (x + y) In(x + y) =0. 24. (y - vx] + y ) dx - x dy = 0; when x = \\/3, y = 1. ANS. X = 9- 6y. 25. (y + x? + y?)dx - xdy = 0; when x = /3, y = 1. ANS. X- = 2y + 1. 26. [x cos' (y/x) - y] dx + xdy = 0; when x = 1, y = */4. ANS, tan (y/x) = In (e/x). 27. (y' + 7xy + 16x]) dx + x' dy = 0; when x = 1, y = 1. ANS. x - y = 5(y + 4x) In x. 28. y' dx + (x2 + 3xy + 4y]) dy = 0; when x = 2, y = 1. ANS. 4(2y + x) In y = 2y - x. 29. xy dx + 2(x2 + 2y') dy = 0; when x = 0, y = 1. ANS. y (3x] + 4y]) = 4. 30. 1(2x3 - xy + y') dx - x'(2x - y)dy = 0; when x = 1, y = 1. ANS. y' In x = 2y2 + xy - x2. 31. y(9x - 2y) dx - x(6x - y)dy = 0; when x = 1, y = 1. ANS, 3x3 - xy - 23 =0. 32. y(x3 + y') dx + x(3x2 - 5y?) dy = 0; when x = 2, y =1. ANS. 2y5 - 2x y' + 3x = 0. 33. (16x + Sy) dx + (3x + y)dy = 0; the curve to pass through the point (1, -3). ANS. y + 3x = (y + 4x) In (y + 4x). 34. v(3x + 20) dx - x' du = 0; when x = 1, v = 2. ANS. 2x* + 2x70 - 30 = 0. 35. (3x2 - 2y?)y' = 2xy; when x = 0, y = -1. ANS. x2 = 2y' (y + 1). 36. From Theorems 1 and 2, page 26, it follows that, if F is homogeneous of degree k in x and y. F can be written in the form (A)