Ordinary Differential Equations/Separable 4

Existence problems 1) f(x,y) has no discontinuities, so a solution exists. has no discontinuities, so the solution is unique. 2) f(x,y) is not defined for the point (-1,10) because ln(x) is not defined. So no solution exists. 3) f(x,y) has discontinuities at y=1 and -1, but not at 0 so a solution exists. has no discontinuities at (0,16) so the solution is unique. 4) f(x,y) has discontinuities at y<0, but not at 1 so a solution exists. is discontinuous at 1, so the solution is not unique 5) f(x,y) has discontinuities at -3 and -4, but not at 0 so a solution exists. has no discontinuities at (5,9) so the solution is unique. 6) f(x,y) has a discontinuity at x=5, so no solution exists. Separable equations 7) 8) 9) 10) 11) 12) Initial value problems 13) 14)