Do not get the same post question. Kindly write in a neat and organize way.

Instruction: using the topic of exact equation in differential equation choose at least 5 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 Test each of the following equations for exactness and solve the equation. The equations that are not exact may, of course, be solved by methods discussed in the preceding sections. 1. (x + 2y) dx + (2x + y)dy = 0. ANS. X' + 4xy + y = c. 2. (2xy - 3x3) dx + (x2 + 2y) dy = 0. ANS. Xy- x+ y =0. 3. (6x + y?) dix + )(2x - 3y) dy = 0. ANS. 3x + xy - y = c. 4. (12 - 2xy + 6x) dx - (x? - 2xy + 2) dy = 0. ANS. xyl - xly + 3x3 - 2y = c. : 5. (2xy - y) dx + (x' + x) dy = 0. ANS. J(x + 1) = ex. 6. (2u' - 3) du + (3u v' - 3u + 40) do = 0. ANS. Buy' - 3u + 20) = c. 7. (cos 2y - 3x y') dx + (cos 2y - 2x sin 2y - 2x y) dy = 0. ANS. # sin 2y + x cos 2y - xy = c. 8. (1 + y' ) dx + (x y + y)dy = 0. ANS. 2 arctan x + In (1 + y') = c. 9. (1 + y' + xy' ) dx + (x- y + y + 2xy)dy =0. ANS. 2x + y (1 + x) = c. 10. (w3 + w23 - =) dw + (2) + w z - w) dz = 0. ANS. (w3 + 17)? = 4wz + c. 11. (2xy - tan y) dx + (x2 - x sec' y) dy = 0. ANS. xy - x tan y = c. 12. (cos x cosy - cot x) dx - sin x sin ydy = 0. ANS. sin x cos y = In jc sin x). 13. (r + sin @ - cos 0) dr + r(sine + cos @) de = 0. ANS. r + 2r(sin 0 - cos 0) = c. 14. x(3xy - 4y' + 6) dx + (x3 - 6xy' - 1) dy = 0. ANS. X y - 2x3y + 3x - y = c. 15. (sin 0 - 2r cost () dr + r cos @(2r sin 0 + 1) do = 0. ANS. rsin 0 - r cos' 0 = c. 16. [2x + y cos (xy)] dx + x cos (xy) dy = 0. ANS. x + sin (xy) = c. 17. 2xy dx + (y' + x) ) dy = 0. ANS. (3x + ') = C. 18. 2xydx + (yz - x) dy = 0. ANS. x + y = cy. 19. (2xy cos (x2) - 2xy + 1] dx + [sin (x]) - x]]dy =0. ANS. y[sin (x]) - x]] = c - x. 20. (2x - 3y) dx + (2y - 3x) dy = 0. ANS. x3 + 2 - 3xy = c. 21. Do exercise 20 by a second method. 22. (xy) + y - x) dx + x(xy + 1)dy = 0. ANS. x23 + 2xy - x3 = c. 23. 3y(x2 - 1) dx + (x' + 8y - 3x)dy = 0; when x = 0, y = 1. ANS. xy(x] - 3) = 4(1 - y3)