Please answer questions 1 , 3 , 8 and 15. Thank you!

In Exercises 1 through 4 solve the given differential equa- 8. 2(x1)y+(x22x+3)cos2y=0 tion by hand and confirm the result by using computer 9. (1+3y2)y+2yln1+x=0. algebra. 10. 2(1cosx)y+3siny=0. 1. 2yy=x(12y) with y(1)=1. 11. (1+x2)yyx(y2+y+1)=0. 2. 2x2y2y+y4=4 with y(1)=3. 12. (x2+9)y2y(4y2)=0 3. (x24)y=x(12y) with y(5)=1. 13. yctgx+2y=4. 4. 2(1+x2)y=(1y2) with y(1)=1. 14. (x+1)y2y=x(y2+4) In Exercises 5 through 14 find the general solution of the In Exercises 15 through 17 derive and then solve the differgiven differential equation. ential equation that determines the orthogonal trajectories 5. (1+x2)y3x(y21)=0 to the given one parameter family of curves 6. e24yy+xsin2y=0. 15. y=b+k(xa) with a and b constants and k a pa- 7. 2(1+x)(1+y)y+(y+2)2=0. rameter. 16. x24y2+y=c with c a parameter. 17. y=Cx2e2s with C a parameter