dy 13. dx dy 14. olve the given differential equation. dx Diving first- that there are several methods of used on a certain type of equation. me proficient in matching solution at 24 of the following problems are ctice in identifying the method or equation. The remaining problems that can be solved by specialized 10. (x²+y)+(x+6) =0 11. (x + y) +(x+2y) =0, y(2)=3 12. (ex+1)=y-ye* excos y-e2y cos x -e- sin y+2e2y sin.x 2x+3y empido find the solution that satisfies it. dy 15. dx +2y=e-2, y(0) = 3 16. dy 3x-2y-y dx 2x+3xy2 17. yey =0 18. dy 2y2+6xy-4 + =0 dx 3x²+4xy+3y2 dy 19. t +(t + 1)y=2 dt ST 20. xy = y+xe 21. dy * Hint: Let u = x². dx 0 x2y+y³ 22. dx -0 23. (3y²+2xy)-(2xy + x²)=0 24. xy+y-y=0, y(1)=2 Chapter Review Problems Miscellaneous Problems. One of the difficulties in solving first- order differential equations is that there are several methods of solution, each of which can be used on a certain type of equation. It may take some time to become proficient in matching solution methods with equations. The first 24 of the following problems are presented to give you some practice in identifying the method or methods applicable to a given equation. The remaining problems involve certain types of equations that can be solved by specialized methods. In each of Problems I through 24, solve the given differential equation. If an initial condition is given, also find the solution that satisfies it. x³-2y 10. (x²+3)+(x+6)=0 11. (x + y)+(x+2y)=0. >(2)=3 12. (e²+1)=y-ye 13. 14. dy dx dy e cos y el cos x -e- sin y+2e sin x +3y 15. +2y=-, y(0)=3 dx 1. dx dy dy 3x²-2y-y x 16. dx 2x + 3xy2 2. dx 2-sin y 17. ye dy 2x+y 3. y(0)=0 18. dy 2y+6xy-4 + =0 dx 3+3y-x dx 3x²+4xy+3y² 4.-3-6x+y-2xy dy 19. +(1+1)y=g dt 5. 2xy + y²+1 20. Kỷ =y+xe dx x²+2xy dy 21. Hint: Let u = x². dx xy+y 6. x +xy 1-y, y(1)=0 dx dy x+y 22. 7. x dz +2y=! sin x dx y(2)=1 xmy 8. 2xy +1 -- x+2y 23. (3y²+2xy)-(2xy + x²)=0 24. xy+y-y=0, y(1)=2 9. (x²+xy-3)+(x²y-2x²)=0