PROBLEM SET B: Determine whether the given function is a solution to the given differential equations. 6. y = sinx + x , dy _ ty = x +2 dx 7. x = 2 cos cost - 3 sin sint , x + x =0 3t 2t d'e 2t 8. 0 = 2e de e dt + 30 =- 2e dt 9. x = cos cos 2t , dt dx 4 tx = sin 2t 10. y =e 2x - 3e. y - 4y = 5e-* PROBLEM SET C: Determine whether the given relation is an implicit solution to the given differential equation. Assume that the relationship does define y implicitly as a function of x and use implicit differentiation. 11. X ty = 4, dy X dx V dy 2xy 12. yy = x +1, dx y-1 13. ety = x - 1, dy e dx e -xy+x 2 dy 14. x - sin sin (x + y) = 1, = 2x sec sec (x + y) - 1. dx 15. sin sin y + xy - x = 2, = 6xy + (y) sinsin y-2(v) 3x- -y