Please refer to the image below

Fig. 15. Particular solutions in Example 5 PROBLEM SET 1.4 1-20 EXACT ODES. INTEGRATING FACTORS 11. -y dx + x dy = 0 Test for exactness. If exact, solve. If not, use an integrating 12. (exty - y) dx + (xetty + 1) dy = 0 factor as given or find it by inspection or from the theorems in the text. Also, if an initial condition is given, determine 13. -3y dx + 2x dy = 0, F(x, y) = y/x* the corresponding particular solution. 14. (x* + y2) dx - xy dy = 0, y(2) = 1 1. x3 dx + y3 dy = 0 2. (x - y)(dx - dy) = 0 15. e *(2 cos y dx - sin y dy) = 0, y(0) = 0 3. - 7 sin wx sinh y dx + cos wx cosh y dy = 0 16. -sin xy (y dx + x dy) = 0, y(1) = T 4. (ev - ye") dx + (xel - e*) dy = 0 17. (cos wx + w sin wx) dx + ex dy = 0, y(0) = 1 5. 9x dx + 4y dy = 0 18. (cos xy + x/y) dx + (1 + (x/y) cos xy) dy = 0 6. e*(cos y dx - sin y dy) = 0 19. e " dex + e *(-e-v + 1) dy = 0, F= exty 7. e-20 dr - 2re-20 de = 0 20. (sin y cosy + x cos?y) dx + x dy = 0 8. (2x + 1/y - y/x2) dix + (2y + 1/x - x/y2) dy = 0 9. (-y/x2 + 2 cos 2x) dx + (1/x - 2 sin 2y) dy = 0 21. Under what conditions for the constants A, B, C, D is (Ax + By) dx + (Cx + Dy) dy = 0 exact? Solve 10. -2xy sin (x2) dx + cos (x2) dy = 0 the exact equation